Calculate percentage of height, radius and volumes of these cylinders

Hyderabad: This article is in continuation to the last article focusing on the percentage topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment jobs. 1. If the radius of a cylinder is decreased by 50% and the height is increased by 50% to […]

Hyderabad: This article is in continuation to the last article focusing on the percentage topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment jobs.

1. If the radius of a cylinder is decreased by 50% and the height is increased by 50% to form a new cylinder, the volume will be decreased by

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a) 75% b) 62.5% c) 25% d) 0%
Ans: b

Solution: 50% = -50/100 = -1/2, 50% = 50/100 = 1/2
Volume = pi r²h
radius –>; 2 : 1
r² –>; 4 : 1
height –>; 2 : 3
8 : 3
-5/8 × 100% = – 62.5%

2. Each of the radius of the base and the height of a right circular cylinder is increased by 10%. The volume of the cylinder is increased by?

a) 19.5% b) 3.31% c) 14.5% d) 33.1%

Ans: d
Solution: 10% = 10/100 = 1/10, 10% = 10/100 = 1/10

Volume = pi r²h

radius –>; 10 : 11

r² –>; 100 : 121

height –>; 10 : 11
Volume –>; 1000 : 1331
331/1000 × 100% = 33.1%

3. If the radius of a cylinder is increased by 120% and its height is decreased by 40%, what is the percentage increase in its volume?
a) 190% b) 190.4% c) 211% d) 211.4%
Ans: b

Solution: 120% = 120/100 = 6/10, 40% = -40/100 = -2/5
Volume = pi r²h
radius –>; 5 : 1
r² –>; 25 : 121
height –>; 4 : 3
Volume –>; 125 : 363

238/125 × 100% = 190.4%

4. If the radius of the cylinder is decreased by 20%, then by how much percent the height must be increased so that the volume of the cylinder remains same?
a) 50.25% b) 56.25% c) 60.25% d) 66.25%
Ans: b

Solution: 20% = -20/100 = -1/5
Volume = pi r²h
radius –>; 5 : 4
r² –>; 25 : 16
height –>; 16 : 25 (volume remains same)
9/16 × 100% = 56.25%

3. Volume of a cylinder is increased by 43% when its height is decreased by 15 5/13%, then find the percentage change in curved surface area of a cylinder?
a) 10% b) 11% c) 12% d) 13%
Ans: a

Solution: 43% = 43/100, 15 5/3% = -2/13
Volume = pi r²h

V/h = r²
V –>; 100 : 143
h –>; 13 : 11

r² –>; 100 × 11 : 13 × 143

r –>; 10 : 13

CSA –>; 10 × 13 : 13 × 11

10 : 11

1/10 × 100% = 10%

4. If the area of the base of a cone is increased by 100%, then the volume increased by

a) 100% b) 141% c) 182% d) 200%

Ans: a
Solution: 100% = 100/100 = 1/1

Area of the base = pi r²

Volume = 1/3 pi r²h
r² –>; 1 : 2

1/1 × 100% = 100%

5. Height of a right circular cone is decreased by 6.25% and its radius is decreased to 15 cm, the volume of a cone is decreased by 40%. Radius of a new cone is how much lesser than previous cone?

a) 3.5cm b) 3.75cm c) 4 cm d) 4.25 cm

Ans: b

Solution: Volume = pi r²h

V/h = r²

V –>; 5 : 3
h –>; 16 : 15
r² –>; 5 × 15 : 16 × 3
25 : 16
r –>; 5 : 4
-1
4 –>; 15cm
1 –>; ?

15/4 = 3.75 cm

6. If the height of a cone is increase by 100%, then its volume is increased by
a) 100% b) 200% c) 300% d) 400%
Ans: a

Solution: 100% = 100/100 = 1/1
Volume = 1/3 pi r²h
height –>; 1 : 2

Volume –>; 1/1 ×100% = 100%

7. If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, the volume of the cone is?
a) increases by 50% b) increase by 25% c) decreases by 50% d) decreases by 25%
Ans: d
Solution: 200% = 200/100 = 2/1, 50% = -50/100 = -1/2

Volume = 1/3 pi r²h

radius –>; 2 : 1
r² –>; 4 : 1
height –>; 1 : 3
Volume –>; 4 : 3
-1/4 × 100% = -25%

8. Each of the height and base radius of a cone is increased by 100%. The percentage increase in the volume of the cone is?

a) 100% b) 300% c) 400% d) 700%

Ans: d
Solution: 100% = 100/100 = 1/1, 100% = 100/100 = 1/1

Volume = pi r²h

radius –>; 1 : 2

r² –>; 1 : 4
height –>; 1 : 2

Volume –>; 1 : 8

7/1 × 100% = 700%

To be continued…