Chapter 11- Mensuration Ex 9.3
Keeping the examination point of view in mind the skmath.in team has prepared NCERT Solutions for Class 8 Maths Chapter 9 Mensuration Exercise 9.3. The NCERT Solutions for chapter Mensuration solutions explains the easy and simple way to solve the problems. By understanding these ways in NCERT Solutions for Class 8, students will be confident while solving such problems found in Chapter 9 Mensuration Exercise 9.3.
1. Given a cylindrical tank, in which situation will you find the surface area, and in which situation will you find the volume
(a) To find how much it can hold.
(b) Number of cement bags required to plaster it.
(c) To find the number of smaller tanks that can be filled with water from it.
Solution:
(a) Volume
(b) Surface area
(c) Volume
2. Diameter of cylinder A is 7 cm, and the height is 14 cm. The diameter of cylinder B is 14 cm, and the height is 7 cm. Without doing any calculations, can you suggest whose volume is greater? Verify it by finding the volume of both cylinders. Check whether the cylinder with greater volume also has a greater surface area.
Solution:
Yes, we can say that volume of cylinder B is greater since the radius of cylinder B is greater than that of cylinder A.
Find the Volume for cylinders A and B
The diameter of cylinder A = 7 cm
The radius of cylinder A = \(7\over 2\) cm
The height of cylinder A = 14 cm
The volume of cylinder\( A = \pi r^2 h
= ({22\over 7} )×({7\over 2})×({7\over 2})×14 = 539\)
The volume of cylinder A is \(539 \text{cm}^3\)
Now, the diameter of cylinder B = 14 cm
The radius of cylinder B = \(14 \over 2\) = 7 cm
And the height of cylinder B = 7 cm
The volume of cylinder \(B = \pi r^2 h
= ({22\over 7})\times 7\times 7\times 7 = 1078\)
The volume of cylinder B is \(1078 \text{cm}^3\)
Find the surface area for cylinders A and B
The surface area of cylinder \(A = 2Ï€r(r+h )
= 2 \times {22\over 7} \times {7\over 2} \times ({7\over 2} + 14) = 385\).
The surface area of cylinder A is \(385 \text{cm}^2\).
The surface area of cylinder \(B = 2Ï€r(r+h)
= 2×({22\over 7})\times 7(7+7) = 616\)
The surface area of cylinder B is \(616 \text{ cm}^2\)
Yes, a cylinder with greater volume also has a greater surface area.
Solution:
The base area of the cuboid = \(180 \text{cm}^2\)
volume of the cuboid = \(900 \text{cm}^3\)
volume of the cuboid = lbh
900 = 180×h
h= \({900\over 180} = 5 \)
Hence, the height of the cuboid is 5 cm.
4. A cuboid is of dimensions 60 cm×54 cm×30 cm. How many small cubes with sides 6 cm can be placed in the given cuboid?
Solution:
Length of the cuboid, l = 60 cm,
Breadth of the cuboid, b = 54 cm
The height of the cuboid, h = 30 cm
Volume of the cuboid \(= lbh = 60 ×54×30 = 97200 \text{cm}^3\)
Volume of the cube = \((\text{Side})^3
= 6×6×6 = 216 \text{cm}^3\)
The number of small cubes \(= {\text{the volume of the cuboid} \over \text{the volume of the cube}} = {97200\over 216} = 450\)
Hence, the required cubes are 450.
5. Find the height of the cylinder whose volume is 1.54 \(\text{m}^3\) and the diameter of the base is 140 cm.
Solution:
The volume of the cylinder \(= 1.54 \text{m}^3 \)
Diameter of the cylinder = 140 cm
Radius ( r )\(= {d\over 2} = {140\over 2} = 70\) cm
The volume of the cylinder = \(\pi r^2 h\)
\({22\over 7}×0.7×0.7×h =1.54 \)
\(h = {(1.54×7)\over (22×0.7×0.7)} \)
\(h = 1\)
Hence, the height of the cylinder is 1 m.
6. A milk tank is in the form of a cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres that can be stored in the tank.
Solution:
The radius of the cylindrical tank, r = 1.5 m Height of the cylindrical tank, h = 7 m
The volume of the cylindrical tank, \(V = \pi r^2 h \)\[ ={22\over 7}×1.5×1.5 ×7\] \[= 49.5 \text{ cm}^3\]\[= 49.5×1000 \text{ litres}\]\[= 49500 \text{ litres }{[∵ 1 \text{ m}^3 = 1000 \text{ litres}]} \]
Hence, the required quantity of milk is 49500 litres.
7. If each edge of a cube is doubled,
(i) how many times will its surface area increase?
(ii) how many times will its volume increase?
Solution:
(i) Let the edge of the cube be \( l\).
The formula for the surface area of the cube, \(A = 6 l^2 \)
When the edge of the cube is doubled, then
The surface area of the cube, say \(A' = 6(2l)^2 = 6×4l^2 = 4(6 l^2)
A' = 4A\)
Hence, the surface area will increase by four times.
(ii) The volume of the cube, \(V = l^3\)
When the edge of the cube is doubled, then
The volume of cube, say \(V' = l^3 = (2l)^3 = 8( l^3)\)
\(V' = 8×V \)
Hence, the volume will increase 8 times.
8. Water is poured into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of the reservoir is \(108 \text{m}^3\), find the number of hours it will take to fill the reservoir.
Solution:
Volume of the reservoir \(= 108 \text{ m}^3\)
\(\displaylines{\text{The rate of pouring water into the cuboidal reservoir } = 60 {\text{ litres}\over \text{minute}} \\ \text{We know }1 \text{ litre} = ({1\over 1000})\text{m}^3 \\ = {60 \over 1000} \text{m}^3 \text{per hour }\\= {(60×60)\over 1000} \text{m}^3 \text{per minute}} \)
\( \displaylines{{(60×60)\over 1000} \text{m}^3 \text{ water filled in reservoir will take = 1 hour } \\ ∴ 1 \text{m}^3 \text{ water filled in reservoir will take} = {1000\over(60×60)} \text{hours}\\∴ 108 \text{m}^3 \text{water filled in reservoir will take} = {(108×1000) \over (60×60)} \text{ hours}\\ = 30 \text{ hours }}\)
Answer: It will take 30 hours to fill the reservoir.
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