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Question 1 of 50
A tank, 50cm by 20cm by 20cm, was completely filled with water. Find the volume of the water in the tank.
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The figure below is made up of 2cm cubes. Find the volume the figure.
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Billy needs to pack as many 4cm wooden cubes as possible into box measuring 31cm by 15cm by 22cm as shown below.
(a) What is the maximum number of wooden cubes that can be packed into the box?
(b) What is the volume of the remaining space in the box after the maximum number of wooden cubes has been packed in?
(b) 355cm$^3$
(b) 3510cm$^3$
(b) 3515cm$^3$
(b) 3520cm$^3$
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(a) 31 ÷ 4 = 7 R 3
15 ÷ 4 = 3 R 3
22 ÷ 4 = 5 R 2
$7 \times 3\times 5 = 105$ cubes
(b) $105 \times 4 \times 4 \times 4 = 6720$
$31 \times 15 \times 22 = 10230$
10230 - 6720 = 3510cm$^3$
(b) 3510cm$^3$
You are Right
(a) 31 ÷ 4 = 7 R 3
15 ÷ 4 = 3 R 3
22 ÷ 4 = 5 R 2
$7 \times 3\times 5 = 105$ cubes
(b) $105 \times 4 \times 4 \times 4 = 6720$
$31 \times 15 \times 22 = 10230$
10230 - 6720 = 3510cm$^3$
Susan arranges some 3cm cubes as shown below. How more such cubes will she need if she wants to form a bigger cube will a volume of 3375$^3$?
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1 cube $\rightarrow$ $3 \times 3 \times 3 = 27$
no cubers needed $\rightarrow$ 3375 ÷ 27 = 125
More $\rightarrow$ 125 – 9 = 116
You are Right
1 cube $\rightarrow$ $3 \times 3 \times 3 = 27$
no cubers needed $\rightarrow$ 3375 ÷ 27 = 125
More $\rightarrow$ 125 – 9 = 116
The total area of the 6 face of a cube is 150cm$^2$. What is the volume of the cube?
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Tank A contain some water. Tank A with a base area of 756.25$^2$, has a water level of 28cm. Tank B is made up of a cuboid with a rectangular base and a cuboid with a square base. The water level in Tank B is 20cm. What is the volume of water in Tank A when the water level is at 14cm?
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10587.5 $\rightarrow$ $14 \times 756.25 = 10587.5$
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10587.5 $\rightarrow$ $14 \times 756.25 = 10587.5$
The solid below is made up of 1cm cubes. How many more of such cubes are needed to from a solid with a volume of 20cm$^3$?
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Dae made the cuboid shown below using cubes of sides 4cm. What is the volume of the cuboid?
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Vol of 1 cube $\rightarrow$ $4 \times 4 \times 4 = 64$cm$^3$
Vol of cuboid $\rightarrow$ $64cm^3 \times 8 = 512$cm$^3$
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Vol of 1 cube $\rightarrow$ $4 \times 4 \times 4 = 64$cm$^3$
Vol of cuboid $\rightarrow$ $64cm^3 \times 8 = 512$cm$^3$
Two containers with some water are shown below. Find the total volume of water in the containers
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Total vol. $\rightarrow$ 250ml + 700ml = 950ml
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Total vol. $\rightarrow$ 250ml + 700ml = 950ml
The diagram below shows the net of a cuboid. It is made up of 2 identical squares and 4 identical rectangles. Find the volume of the cuboid.
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1 side square $\rightarrow$ 24cm – 14cm = 10cm
Volume $\rightarrow$ $10cm \times 10cm \times 12cm = 200$cm$^3$
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1 side square $\rightarrow$ 24cm – 14cm = 10cm
Volume $\rightarrow$ $10cm \times 10cm \times 12cm = 200$cm$^3$
The figure below shows a container with some water. What is the best estimate of the volume of water in the container?
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The length of cube is 7cm. what is the volume of the cube?
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A cuboid has a square base of sides 14cm each and a height od 7cm. What is the volume of the cuboid?
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The length of a cube is 9cm. What is the volume of the cube?
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Tank A and Tank B are regular containers. Tank A was filled with water to a height of 22cm.
(a) what was the volume of water Tank A at first?
(b) The water in Tank A was poured into Tank B such that the height of the water in Tank A was 3 times the height of the water in Tank B. Find the volume of water of Tank B.
(b) 920cm$^3$
(b) 940cm$^3$
(b) 960cm$^3$
(b) 980cm$^3$
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(a) $22cm \times 12cm \times 20cm = 5280$cm$^3$
$20cm \times 12cm \times 3cm = 720$cm$^3$
$16cm \times 10cm \times 1cm = 160$cm$^3$
720cm$^2$ + 160cm$^3$ = 880cm$^3$
5280cm$^3$ ÷ 880cm$^3$ = 6
(b) $6 \times 160cm^3 = 960$cm$^3$
(b) 960cm$^3$
You are Right
(a) $22cm \times 12cm \times 20cm = 5280$cm$^3$
$20cm \times 12cm \times 3cm = 720$cm$^3$
$16cm \times 10cm \times 1cm = 160$cm$^3$
720cm$^2$ + 160cm$^3$ = 880cm$^3$
5280cm$^3$ ÷ 880cm$^3$ = 6
(b) $6 \times 160cm^3 = 960$cm$^3$
Find the volume of a cube which has a total surface are of 96cm$^2$.
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The figure below shows the net of a solid. What is the volume of the solid?
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H = 3cm, B = $(18 – 3 – 3)$ ÷ 2 = 6cm, L = 7cm
volume = $7 \times 6 \times 3 = 126$cm$^3$
You are Right
H = 3cm, B = $(18 – 3 – 3)$ ÷ 2 = 6cm, L = 7cm
volume = $7 \times 6 \times 3 = 126$cm$^3$
A rectangular block of wood measuring 50cm by 5cm was cut into five equal pieces. What was the volume of each piece of wood.
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Every cube has 6 faces. 9 identical cubes have a total surface area of 2646cm$^2$. Find the volume of one cube.
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2646 ÷ 9 = 294
294 ÷ 6 =49
$7 \times 7 = 49$
$7 \times 7 \times 7 = 343$
You are Right
2646 ÷ 9 = 294
294 ÷ 6 =49
$7 \times 7 = 49$
$7 \times 7 \times 7 = 343$
J, K and L are three rectangular containers. The case area of J, K and L are 120cm$^2$, 50cm$^2$ and 80 cm$^2$ respectively. At first j contained 4960 cm$^3$ of water while K and L were empty as shown below.
Minah then poured some water from J into K and L. After that, the height of water level in L was 4cm lower than that in K and 8cm lower than in J. Find the difference in the volume of water between J and L in the end.
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$4 \times 50 = 200$
$8 \times 120 = 960$
4960 – 200 – 960 = 3800
$120 \times H + 50 \times H + 80 \times H = 3800$
H = 23.2
$120 \times 23.2 – 80 \times 15.2 = 1568$
You are Right
$4 \times 50 = 200$
$8 \times 120 = 960$
4960 – 200 – 960 = 3800
$120 \times H + 50 \times H + 80 \times H = 3800$
H = 23.2
$120 \times 23.2 – 80 \times 15.2 = 1568$
The figure below shows a piece of cardboard of length 15cm. When the shaded rectangles A, B, D and square C are cut out, the remaining parts form the net of cuboid. Given that the area of A is 10cm$^2$ and the area of C is 81cm$^2$. Find the volume of the cuboid.
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$\sqrt(81)=9$
18 ÷ 9 = 2
$9 \times 2 \times 2 = 36$cm$^3$
You are Right
$\sqrt(81)=9$
18 ÷ 9 = 2
$9 \times 2 \times 2 = 36$cm$^3$
The net of the cube shown below has a perimeter of 98cm. Find the volume of the cube.
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98 ÷ 124 = 7
$7 \times 7 \times 7 = 343$cm$^3$
You are Right
98 ÷ 124 = 7
$7 \times 7 \times 7 = 343$cm$^3$
The figure shows a container with a square base and a height of 15cm. Find the volume of the container.
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A rectangular block of wood is 20cm by 15cm by 16cm. What is the greatest number of 2cm cube that be cut from it?
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The solid shown below are formed by cubes of different dimensions. Find the difference in volume between two solids.
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A solid of hight 15cm has a square base of 5cm. Find its volume.
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$5 \times 5 \times 15 = 375$cm$^3$
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$5 \times 5 \times 15 = 375$cm$^3$
The figure below shows a solid that is made up of 2cm cubes. The cubes are stacked on top of one another. How many more such cubes are required from a larger solid with a volume of 192 cm$^3$?
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The solid below is made up of 1cm cubes. What is the volume of the solid?
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10cm$^3$ $\rightarrow$ $1 \times 1 = 1$, $1 \times 10 = 10$
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10cm$^3$ $\rightarrow$ $1 \times 1 = 1$, $1 \times 10 = 10$
Which of the following is same as $\frac{3}{50}$m?
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The cube below, not drawn to scale has a length of 7cm. what is its volume?
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343cm$^3$ $\rightarrow$ $7cm \times 7cm \times 7cm = 343$
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343cm$^3$ $\rightarrow$ $7cm \times 7cm \times 7cm = 343$
The total volume of 8 identical cans is 2.56. What is the total volume of 2 cans of soda in milliliters?
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The area of each face of a cube is 49cm$^2$. What is the volume of the cube?
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If the shaded part of the cube shown is 64cm$^2$. What is the volume of the cube?
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The net of a cuboid is shown below. The base has an area of 55 cm$^2$. Find the volume of the cuboid.
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What is the volume of the cuboid shown below?
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Tank X, measuring 40cm by 30cm by 98cm, is $\frac{3}{4}$ filled with water. Tank Y, with a square base of side 50cm, is empty. Water from Tank X is slowly poured into Tank Y until the water level in Tank X is 2 times the height of the water level in Tank Y.
What is the height of the water level in Tank X?
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$40 \times 30 = 1200$
$1200 \times 2 = 2400$
$50 \times 50 = 2500$
2500 + 2400 = 4900
$\frac{3}{4}m \times 98 \times 40 \times 30 = 88200$
88200 ÷ 4900 = 18
$18 \times 2 = 36cm$
You are Right
$40 \times 30 = 1200$
$1200 \times 2 = 2400$
$50 \times 50 = 2500$
2500 + 2400 = 4900
$\frac{3}{4}m \times 98 \times 40 \times 30 = 88200$
88200 ÷ 4900 = 18
$18 \times 2 = 36cm$
The diagrams below show the front view and the back view of a cuboid. The cuboid is made up of a total of 16 white and shaded 1cm cubes. What is the volume of the shaded cubes?
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A cuboid measures 1.1m by 40cm by 10cm. Find its volume. A cuboid measures 1.1m by 40cm by 10cm. Find its volume.
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The diagram below shows a tank made of some identical sections. Figure A shows one section of the tank.
Find the volume of figure A.
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$20 \times 10 \times 2 = 400$
$16 \times 2 \times 10 = 320$
320 + 400 = 720cm$^3$
You are Right
$20 \times 10 \times 2 = 400$
$16 \times 2 \times 10 = 320$
320 + 400 = 720cm$^3$
A tank was $\frac{2}{3}$ filled with water to a height of 20cm.
(a) What is the capacity of the tank?
(b) When a glass ball was dropped into the tank, the height of the water level was 1.5cm from the brim of the tank. Find the volume of the glass ball.
(b) 264cm$^3$
(b) 268cm$^3$
(b) 270cm$^3$
(b) 272cm$^3$
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(a) $\frac{2}{3}$ $\rightarrow$ $20 \times 20 \times 16 = 6400$
$\frac{3}{3}$ $\rightarrow$ $6400 ÷ 2 \times 3 = 9600$
(b) 9600 ÷ 20 ÷ 16 = 30
30 – 1.5 = 28.5
$28.5 \times 20 \times 16 = 9120$cm$^3$
9120 – 6400 = 2720 cm$^3$
(b) 272cm$^3$
You are Right
(a) $\frac{2}{3}$ $\rightarrow$ $20 \times 20 \times 16 = 6400$
$\frac{3}{3}$ $\rightarrow$ $6400 ÷ 2 \times 3 = 9600$
(b) 9600 ÷ 20 ÷ 16 = 30
30 – 1.5 = 28.5
$28.5 \times 20 \times 16 = 9120$cm$^3$
9120 – 6400 = 2720 cm$^3$
The figure below shows a cuboid. The shaded face is a square of area 64cm$^2$. What is the volume of the cuboid?
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The total surface area of a cube is 96cm$^2$. Find the volume of the cube.
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The figure below shows the net of a cuboid made of 4 identical rectangles and 2 identical squares. Find the volume of the cuboid.
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725cm$^3$ $\rightarrow$ Length $\rightarrow$ 34 – 5 = 29, $5 \times 5 \times 29 = 725$
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725cm$^3$ $\rightarrow$ Length $\rightarrow$ 34 – 5 = 29, $5 \times 5 \times 29 = 725$
The figure below shows the net of a cuboid with a square base. Find the volume of the cuboid.
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The area of one face of a cube is 49cm$^2$. What is the volume of the cube?
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The net of a cuboid is made up of 2 squares and 4 rectangles as shown below. The area each square is 100cm$^2$. Given that the total surface area of the net is 280cm$^2$. What is the volume of the cuboid?
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The figure shows a solid made up of identical cubes. The side of each cube is 2 cm. Find the Volume of the solid.
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The figure below shows the net of a box. Three of its faces had area 6cm$^2$, 12cm$^2$ and 18cm$^2$ as shown. Find the volume of the box after the net was folded.
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$6 \times 3 \times 2 = 36$cm$^3$
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$6 \times 3 \times 2 = 36$cm$^3$
The figure below shows a solids a solid that is made up of 2cm cubes. The cubes are stacked o top of one another. How many more such cubes are required to form a large solid with a volume of 192cm$^3$.
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Miss Lim filled the container shown below with water to a height of 25cm at first. What was the volume of water in the container at first?
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Vol $\rightarrow$ $60 \times 20 \times 20 \times 25 = 30,000$cm$^3$
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Vol $\rightarrow$ $60 \times 20 \times 20 \times 25 = 30,000$cm$^3$
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