The ratio of height and diameter of a right circular cone is 3:2 and i

1.	The ratio of height and diameter of a right circular cone is 3:2 and its volume is 1078 cm3. Then find the height of the right circular cone.1. 20 cm2. 31 cm3.21 cm4. 27 cm
Answer» Correct Answer - Option 3 : 21 cm Given: The ratio of height and diameter of the right circular cone = 3 : 2 The volume of cone = 1078 cm³ Formula used: The volume of right circular cylinder = 1/3 × π × radius² × height Calculation: Let the radius be ‘r’ and the height be ‘h’. r = diameter/2 = 2x/2 = x h = 3x The volume of right circular cylinder = 1/3 × π × r² × h ⇒ 1/3 × π × r² × h = 1078 ⇒ 1/3 × π × x² × 3x = 1078 ⇒ x³ = 49 × 7 ⇒ x³ = 7³ ⇒ x = 7 ⇒ height of cone = 3x = 3 × 7 = 21 cm. ∴ the height of the right circular cone is 21 cm.

The ratio of height and diameter of a right circular cone is 3:2 and its volume is 1078 cm3. Then find the height of the right circular cone.1. 20 cm2. 31 cm3.21 cm4. 27 cm

Answer» Correct Answer - Option 3 :

21 cm

Given:

The ratio of height and diameter of the right circular cone = 3 : 2

The volume of cone = 1078 cm³

Formula used:

The volume of right circular cylinder = 1/3 × π × radius² × height

Calculation:

Let the radius be ‘r’ and the height be ‘h’.

r = diameter/2 = 2x/2 = x

h = 3x

The volume of right circular cylinder = 1/3 × π × r² × h

⇒ 1/3 × π × r² × h = 1078

⇒ 1/3 × π × x² × 3x = 1078

⇒ x³ = 49 × 7

⇒ x³ = 7³

⇒ x = 7

⇒ height of cone = 3x = 3 × 7 = 21 cm.

∴ the height of the right circular cone is 21 cm.

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