revision on volume - jimmy maths · 2020. 7. 17. · revision on volume section a: for each...
TRANSCRIPT
www.jimmymaths.com
1 | P a g e
Revision on Volume
Section A: For each question, four options are given. (10 marks)
(1) Cubes of side 1cm are stacked in the corner of a box as shown below.
How many more cubes are needed to make it into a cube of side 5-cm.
(A) 12 (B) 14 (c) 114 (D) 125
(2) The figure below shows a cubical box with a volume of 1331 cm³. What is its based
area?
(3) Which of the following is the same as 5030 ml?
(A) 50 L 3ml (B) 5 L 30ml (C) 5 L 3ml (D) 50 L 30ml
(4) A tank, 40cm by 30cm by 15cm, was completely filled with water. Find the volume
of water in the tank.
(A) 600cm³ (B) 1200cm³ (C) 1800cm³ (D) 18000cm³
(5) Peter wants to pack identical cuboids into a rectangular box shown below.
(A)210 (B) 196 (C) 180 (D) 135
(A) 11cm²
(B) 22cm²
(C) 33cm²
(D) 121cm²
21cm
12cm
15cm
3cm 3cm
m
2cm
www.jimmymaths.com
2 | P a g e
(6) A cuboid has a volume of 216cm³ has a base area of 24cm². What is the height of the
cuboid?
(A) 6cm
(B) 9cm
(C) 24cm
(D) 192cm
(7) A cubical tank of edge 10cm was 1 8⁄ filled with water.
How much more water was needed to filled half of the tank?
(A) 125cm³
(B) 1000cm³
(C) 500cm³
(D) 375cm³
(8) What is the volume of a cuboid with a square base of 6cm and a height of 9cm?
(A) 54cm³
(B) 96cm³
(C) 216cm³
(D) 324cm³
(9) A cube has a volume of 64cm³. When the length of every edge of the cube is doubled,
what is the difference between the new volume and the original volume of the cube?
(A) 128cm³
(B) 196cm³
(C) 4096cm³
(D) 448cm³
(10) The total surface area of a cube equivalent to its volume. Find the volume of the
cube.
(A) 216cm³
(B) 125cm³
(C) 64cm³
(D) 27cm³
www.jimmymaths.com
3 | P a g e
Section B
Questions 11 to 15 carry 1 mark each. Questions 16 -20 carry 2 marks each. Show your workings clearly in the space provided for each question and write your answers in the space provided. For questions which require units, give your answers in the units stated. (15 marks) (11) The volume of a cube is 125 cm³. What is the area of one of its faces?
Ans:_______________________
(12) Find the volume of a container with a square base of 8 cm and a height of 11 cm.
Ans:_______________________
(13) A rectangular tank contains 1560 ml of water when it is 2 3⁄ full. Find the base
area of the tank if the height is 12 cm.
Ans:_______________________
(14) The solids below are formed by cubes of different dimensions. Find the
difference in volume between the two solids
Ans:_______________________
(15) A rectangular tank was half filled with water. When 7.8 L of water was added, it
becomes 4 5⁄ filled. What was the height of the tank if its base area was 500cm²?
Ans:_______________________
www.jimmymaths.com
4 | P a g e
(16) A rectangular block of wood measuring 15cm by 24cm by 17cm. What is the
greatest number of 2-cm cube that can be cut from it?
Ans:_______________________
(17) A rectangular tank measures 45cm by 40cm by 36cm. It contains 20 L of water.
How many more litres of water would be needed to fill the tank to 3 4⁄ of its height?
Ans:_______________________
(18) A container measuring 12cm by 15cm contains 972 ml of water. If the height of
the water is 3 5⁄ that of the container, what is the height of the container?
Ans:_______________________
(19) A cubical tank of height 30cm is completely filled with water. All the water was
transferred from the cubical tank into a rectangular container with a square base of
360cm². What is the water level in the rectangular container?
Ans:_______________________
(20) 9 identical cubes have a total surface area of 4374cm². Find the volume of 1 cube.
Ans:_______________________
www.jimmymaths.com
5 | P a g e
Section C
Show your working clearly in the space provided for each question and write the answer in the space provided. The number of marks available is shown in the brackets ( ) at the end of each questions or part questions. (36 marks)
(21) The fish tank below contains water to a height of 5cm. 3.584 L of water was
added into the tank. The tank is now 3 4⁄ filled with water. Find the height of the
container. (3m)
Ans:_______________________ (22) An empty container, 44cm by 24cm by 47cm has a thickness of 2cm around it, as
shown in the figure. Given that water from the tap flow into the container at a rate
of 3 L per minute, how long does it take for the tank to be 3 4⁄ filled?
Ans:_______________________
www.jimmymaths.com
6 | P a g e
2 litres
(23) A tank, with a rectangular base measuring 22cm by 18cm, was 2 3⁄ filled with
water to a height of 20cm.
(a) What is the capacity of the tank? (1m)
(b) When a metal ball was dropped into the tank, the height of the water was
1.5cm from the brim of the tank. Find the volume of the metal ball. (2m)
Ans (a) _______________________
(b)_______________________ (24) In the figure below, Tank X is filled with water to a height of 8cm. Some water in
A is poured into Tank Y until the height of the water level in both tank become the
same. Find the height of the water level in Tank Y. (3m)
Ans:_______________________
www.jimmymaths.com
7 | P a g e
(25) The figure below shows a water tank that is 7 8⁄ filled with water. It is formed by
placing 2 containers on top of one another. The top container is a cuboid with
square base 8cm and height 36cm. The bottom container is also a cuboid of square
base 12cm and a height of 18cm. Find the height of water from the base of the
container. (Give your answer to 2 decimal place) (4m)
Ans:_______________________
(26) Jane filled a tank measuring 85cm by 30cm by 48cm with some water. The tank
is enclosed and tilted as shown in Figure B, such that it is resting on the 30cm edge.
The water level reached the half way mark of the length of the base.
(a) What is the capacity of the tank? (1m)
(b) How much more water is needed to fill the tank in Figure A to its brim? (1m)
(c) When Jane rests the tank on the horizontal position as shown in Figure A,
what would be the height of the water? (2m)
Ans (a) _______________________
(b)_______________________
(c) ______________________
www.jimmymaths.com
8 | P a g e
(27) Danny poured some water into Tank A and Tank B until the water levels in both
tanks were the same. He then realised that the total volume of water in A and B was
20.8l. He then poured another 1.2 L of water into Tank A to fill it to its brim. What
was the height of A? (4m)
Ans:_______________________ (28) Mei has two rectangular tanks. Tank A has a rectangular base measuring 42cm
by 6cm. Tank B has a rectangular base measuring 14cm by 3cm, Mei poured some water into the two tanks till the height of the water in both tanks are the same. If the difference in volume of water in both tank is 1400cm³, what is the volume of water in Tank B? (4m)
Ans:_______________________
www.jimmymaths.com
9 | P a g e
(29) The diagram below shows a tank made with some sections. Figure A show one section of the tank.
(a) Find the volume of figure A (2m)
(b) 4780 cm³ of water was poured into the tank. Find the water level in the tank.
Ans (a) _______________________
(b)_______________________
www.jimmymaths.com
10 | P a g e
(30) A rectangular tank measuring 40cm by 30cm by 40cm was1 6⁄ filled with water. At
1330h, Tap A with water flowing out at a rate of 3 L per minute was turned on. At 1332h,
Tap B was turned on to drain water out at a fixed rate. At 1343 h, the tank was 75%
filled with water. At what time would the tank be filled to the brim? (5m)
Ans:_______________________
www.jimmymaths.com
11 | P a g e
Answer Key for Volume
Section A
(1) C (2) D (3) B (4) D (5) A
(6) B (7) D (8) D (9) D (10) A
Section B
(11) 25 cm2 (12) 704 cm3 (13) 195 cm2 (14) 1005 cm3 (15) 52 cm2
(16) 672 (17) 28.6 L (18) 9 cm (19) 75 cm (20) 729 cm3
Section C
(21) 12 cm (22) 12 min (23a) 11880 cm3 (23b) 3366 cm3 (24) 2 cm
(25) 44.44cm (26a) 122400cm³ (26b) 91800cm³ (26c) 12cm
(27) 32 cm (28) 280cm³ (29a) 760 cm3 (29b) 25 cm
(30) 1349h