If radius of a cone is increased by 30% and height increased by 20%, t

1.	If radius of a cone is increased by 30% and height increased by 20%, then what is the ratio of new volume to initial volume?1. 250 : 50.72. 50.7 : 2503. 507 : 2504. 250 : 5075. None of these
Answer» Correct Answer - Option 3 : 507 : 250 Given: Increase in radius of cone = 30% Increased in height of cone = 20% Formula used: V = (1/3) × π × r² × h where, V = volume of cone r = radius of cone h = height of cone Calculations: Let the initial radius and height of the cone be r, h. Initial volume = (1/3) × π × r2 × h New radius = r + (r × 30%) ⇒ 13r/10 New height = h + (h × 20%) ⇒ 6h/5 New volume = (1/3) × π × (13r/10)2 × (6h/5) ⇒ (1/3) × π × (169r²/100) × (6h/5) ⇒ (1/3) × π × r2 × h × (169/100) × (6/5) ⇒ (Initial volume) × (169/100) × (6/5) (New volume)/(Initial volume) = 507/250 ∴ The ratio of new volume to initial volume is 507 : 250.

If radius of a cone is increased by 30% and height increased by 20%, then what is the ratio of new volume to initial volume?1. 250 : 50.72. 50.7 : 2503. 507 : 2504. 250 : 5075. None of these

Answer» Correct Answer - Option 3 : 507 : 250

Given:

Increase in radius of cone = 30%

Increased in height of cone = 20%

Formula used:

V = (1/3) × π × r² × h

where,

V = volume of cone

r = radius of cone

h = height of cone

Calculations:

Let the initial radius and height of the cone be r, h.

Initial volume = (1/3) × π × r2 × h

New radius = r + (r × 30%)

⇒ 13r/10

New height = h + (h × 20%)

⇒ 6h/5

New volume = (1/3) × π × (13r/10)2 × (6h/5)

⇒ (1/3) × π × (169r²/100) × (6h/5)

⇒ (1/3) × π × r2 × h × (169/100) × (6/5)

⇒ (Initial volume) × (169/100) × (6/5)

(New volume)/(Initial volume) = 507/250

∴ The ratio of new volume to initial volume is 507 : 250.

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