If the radius of the base of a cone and its height is increased by 10%

1.	If the radius of the base of a cone and its height is increased by 10%. Then the volume of the cone increased by:1. 33%2. 33.1%3. 21%4. 21.1%
Answer» Correct Answer - Option 2 : 33.1% Given: Increase in radius, R’ = 10% Increase in height, H’ = 10% Formula used: Volume of cone = 1/3 × πr²h, where r is the radius of base and h is the height of the cone. Calculation: Let V be the volume of the original cone, R and H are the original radius and original height respectively. Original volume, V = 1/3 × πR²H New radius, R’ = (100 + 10)% of original radius ⇒ R’ = 110/100 × R ⇒ R’ = 11/10 × R New height, H’ = (100 + 10)% of original height ⇒ H’ = 110/100 × H ⇒ H’ = 11/10 × H New volume, V’ = 1/3 × π × (R’)2 × H’ ⇒ V’ = 1/3 × π × (11/10 × R)² × (11/10 × H) ⇒ V’ = (1/3 × πR²H) × 1331/1000 ⇒ V’ = V × 1331/1000 Increased volume = (V’ – V)/V × 100 ⇒ Increased volume = (V × 1331/1000 – V)/V × 100 ⇒ Increased volume = 33.1 ∴ The volume is increased by 33.1%.

If the radius of the base of a cone and its height is increased by 10%. Then the volume of the cone increased by:1. 33%2. 33.1%3. 21%4. 21.1%

Answer» Correct Answer - Option 2 : 33.1%

Given:

Increase in radius, R’ = 10%

Increase in height, H’ = 10%

Formula used:

Volume of cone = 1/3 × πr²h, where r is the radius of base and h is the height of the cone.

Calculation:

Let V be the volume of the original cone, R and H are the original radius and original height respectively.

Original volume, V = 1/3 × πR²H

New radius, R’ = (100 + 10)% of original radius

⇒ R’ = 110/100 × R

⇒ R’ = 11/10 × R

New height, H’ = (100 + 10)% of original height

⇒ H’ = 110/100 × H

⇒ H’ = 11/10 × H

New volume, V’ = 1/3 × π × (R’)2 × H’

⇒ V’ = 1/3 × π × (11/10 × R)² × (11/10 × H)

⇒ V’ = (1/3 × πR²H) × 1331/1000

⇒ V’ = V × 1331/1000

Increased volume = (V’ – V)/V × 100

⇒ Increased volume = (V × 1331/1000 – V)/V × 100

⇒ Increased volume = 33.1

∴ The volume is increased by 33.1%.