Chapter 11 Mensuration Exercise 11.4
Question 1: Given a cylindrical tank, in which situation will you find surface area 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:
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: The volume of Cylinder B is greater than cylinder A because Cylinder B has a bigger diameter.
Given
Cylinder A
diameter = 7 cm
height = 14 cm
Cylinder B
diameter = 14 cm
height = 7 cm
To find
Volume and surface area of both cylinders
Formula
Volume of cylinder = πr²h
TSA of cylinder = 2πr(h + r)
Working
• Cylinder A
→ Volume
= 22/7 × 3.5 × 3.5 × 14
= 22 × 3.5 × 3.5 × 2
= 22 × 35/10 × 35/10 × 2
= 11 × 7 × 7
= 539 cm³
→ TSA
= 2 × 22/7 × 3.5(14 + 3.5)
= 2 × 22/7 × 3.5 × 17.5
= 2 × 22/7 × 35/10 × 175/10
= 11 × 35
= 385 cm²
• Cylinder B
→ Volume
= 22/7 × 7 × 7 × 7
= 22 × 7 × 7
= 1078 cm³
→ TSA
= 2 × 22/7 × 7(7 + 7)
= 2 × 22 × 14
= 616 cm²
Question 3: Find the height of a cuboid whose base area is 180 cm² and volume is 900 cm³?
Answer:
Given
Cuboid
base area = 180 cm²
volume = 900 cm³
To find
Height of a cuboid
Formula
General formula of volume = base area × height
Working
= a × 180 = 900
= a = 900/180
= a = 5 cm
Therefore, the height of cuboid is 5 cm.
Question 4: A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
Answer:
Given
Cuboid
length = 60 cm
breadth = 54 cm
height = 30 cm
Small cube side length = 6 cm
To find
Number of small cubes that can be placed into cuboid
Formula
Volume of cuboid = lbh
Volume of cube = s³
Working
Volume of cuboid = ?
= 60 × 54 × 30
= 97200 cm³
Volume of small cube = ?
= 6³
= 216 cm³
Number of small cubes that can be fit in cuboid = ?
= 97200/216
= 450 small cubes
Therefore, 450 small cubes can be placed into the cuboid.
Question 5: Find the height of the cylinder whose volume is 1.54 m³ and diameter of the base is 140 cm?
Answer:
Given
Cylinder
diameter = 140 cm
volume = 1.54 m³
To find
Height of cylinder
Formula
General formula of volume = base area × height
Area of circle = πr²
Working
Area of base of cylinder = ?
= 22/7 × 70 × 70
= 22 × 10 × 70
= 15400 cm²
Height of cylinder = ?
(1 m³ = 1000000 cm³)
= 15400 × h = 1540000
= h = 1540000/15400
= h = 100 cm
Therefore, the height of cylinder is 100 cm.
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 litres that can be stored in the tank?
Answer:
Given
Milk tank in form cylinder
radius = 1.5 m
height = 7 m
To find
The quantity of milk that can be stored in tank
Formula
Volume of cylinder = πr²h
1 m³ = 1000 litres
Working
= 22/7 × 1.5 × 1.5 × 7
= 22 × 1.5 × 1.5
= 22 × 15/10 × 15/10
= 49.5 m³
1 m³ = 1000 litre
= 49.5 × 1000
= 49500 litres
Therefore, the quantity of milk in litres that can be stored in the tank is 49500 litres.
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 x cm.
If the edge is doubled = x + x = 2x cm
Original surface area = 6 × (x)²
= 6x² cm²
If the edge is doubled, surface area = 6 × (2x)²
= 24x² cm²
Ratio = If edge is doubled surface area:original surface area
= 24x²:6x²
= 24x²/6x²
= 4 times
Therefore, the new surface area of cube will be 4 times more if the edge is doubled.
ii)
Let the edge of cube be x cm.
If the edge is doubled = x + x = 2x cm
Original volume = (x)³
= x³ cm³
If the edge is doubled, surface area = (2x)³
= 8x³ cm³
Ratio = If edge is doubled volume:original volume
= 8x³:x³
= 8x³/x³
= 8 times
Therefore, the new volume of cube will be 8 times more if the edge is doubled.
Question 8: Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 m³, find the number of hours it will take to fill the reservoir.
Answer:
Given
Volume of reservoir = 108 m³
Speed of water flowing = 60 litres per minute
To find
The number of hours it will take to fill reservoir
Formula
1 m³ = 1000 litres
Working
= 108 × 1000
= 108000 litres
Time taken to fill the reservoir = ?
= 108000/60
= 1800 minutes required
1 hour = 60 minutes
= 1800/60
= 30 hours
Therefore, it will take 30 hours to fill the reservoir.
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