Class 8 - Mathematics
Algebraic Expressions and Identities - Exercise 11.4
Top Block 1
Question :1.Given a cylindrical tank, in which situation will you find surface are and in which situation 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.
Answer :
We find area when a region covered by a boundary, such as outer and inner surface area of a cylinder, a cone, a sphere and surface of wall or floor.
When the amount of space occupied by an object such as water, milk, coffee, tea, etc., then we have to find out volume of the object.
(a) Volume (b) Surface area (c) Volume
Question :2. Diameter of cylinder A is 7 cm and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area.
Answer :
Yes, we can say that volume of cylinder B is greater, since radius of cylinder B is greater than that of cylinder A (and square of radius gives more value than previous).
Diameter of cylinder A = 7 cm
⇒ Radius of cylinder A = 7⁄2 cm
And Height of cylinder A = 14 cm
∴ Volume of cylinder A = πr2𝒽
= 22⁄7 x 7⁄2 x 7⁄2 x 14
= 539cm²
Now Diameter of cylinder B = 14 cm
⇒ Radius of cylinder B = 14⁄2 = 7 cm
And Height of cylinder B = 7 cm
∴ Volume of cylinder A = πr2𝒽
= 22⁄7 x 7 x 7 x 7
= 1078 cm²
Total surface area of cylinder A
= πr(2𝒽 + r) [∵ It is open from top]
= 22⁄7 x 7⁄2 x (2 x 14 + 7⁄2) x 14
= 11 x (28 + 22⁄7
= 11 x 63⁄7
= 346.5 cm²
Total surface area of cylinder B
= πr(2𝒽 + r) [∵∵ It is open from top]
= 22⁄7 x 7 (2 x 7 + 7)
= 22 x (14 + 7) = 22 x 21 = 462
Yes, cylinder with greater volume also has greater surface area.
Question :3. Find the height of a cuboid whose base area is 180cm² and volume is 900cm²?
Answer :
Given: Base area of cuboid = 180 cm² and Volume of cuboid = 900 cm²
We know that,
Volume of cuboid = 𝓁 x 𝒷 x 𝒽
⇒ 900 = 180 x 𝒽 [∵ Base area = 𝓁 x 𝒷 = 180 (given)]
𝒽 = 900⁄180 = 5 m
Hence the height of cuboid is 5 m.
Question :4. A cuboid is of dimensions 60 cm X 54 cm X 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
Answer :
Given: Length of cuboid 𝓁 = 60 cm, Breadth of cuboid 𝒷 = 54 cm and
Height of cuboid 𝒽 = 30 cm
We know that, Volume of cuboid
= 𝓁 x 𝒷 x 𝒽 = 60 x 54 x 30 cm³
And Volume of cube = (Side)³
= 6 x 6 x 6 cm³
∴ Number of small cubes
= (Vertical of Cuboid)⁄(Volume of Cube) = (60 x 54 x 30)⁄(6 x 6 x 6)
= 450
Hence required cubes are 450.
Question :5. Find the height of the cylinder whose volume if 1.54cm² and diameter of the base is 140 cm.
Answer :
Given: Volume of cylinder = 1.54m³ and Diameter of cylinder = 140 cm
Mddle block 1
Question :6. A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in liters that can be stored in the tank.
Answer :
Given: Radius of cylindrical tank r = 1.5 m and Height of cylindrical tank 𝒽 = 7 m
Volume of cylindrical tank = πr²𝒽
= 3.14 x 1.5 x 1.5 x 7 = 49.5 cm³
= 49.5 x 1000 liters
[∵ 1m³ = 1000 liters]
= 49500 liters
Hence required quantity of milk is 49500 liters.
Question :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?
Answer :
(i) Let the edge of cube be 𝓁
Since, Surface area of the cube (A) = 𝓁²
When edge of cube is doubled, then
Surface area of the cube (A’)
=6 (2𝓁)² = 6 x 4𝓁² = 4 x 6𝓁²
A’ = 4 x A
Hence surface area will increase four times.
(ii) Volume of cube (V) = 𝓁³
When edge of cube is doubled, then
Volume of cube (V’) = (2𝓁)³ = 8𝓁³
V’ = 8 x V
Hence volume will increase 8 times.
Question :8. Water is pouring into a cuboidal reservoir at the rate of 60 liters per minute. If the volume of reservoir is 108, find the number of hours it will take to fill the reservoir.
Answer :
Given: volume of reservoir = 108 m³
Rate of pouring water into cuboidal reservoir = 60 liters/minute
