Question

if the ratio of the radius of the base and height of the cone is 5:12 and its volume is 314m^3 fi d its perpendicular height and slant height ​

Answer 1

Given:

• The ratio of the radius of the base and height of the cone is 5:12.
• Its volume is 314m^3.

To find:

• find its perpendicular height and slant height ?

Solution:

• Let height of the cone be h.

Here,

• Base = Radius = 5x
• Height = Perpendicular = 12x
• Volume = 314m³

• Let radius of the cone be r.

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« Now, Let's find perpendicular height(12x),

→ Volume of cone = 1/3 × πr²h

→ 314 = 1/3 × 22/7 × (5x)² × 12x

→ 314 = 1/3 × 3.14 × 25x² × 12x

→ 314 = 1 × 3.14 × 25x² × 4x

→ 3.14 × 100 x³ = 314

→ x³ = 1

→ x = 1

Therefore,

• Height = 12x = 12 × 1 = 12cm
• Radius = 5x = 5 × 1 = 5cm

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Now, Let's find slant height,

• Let slant height be s.

→ s² = h² + r²

→ s² = (12)² + (5)²

→ s² = 144 + 25

→ s² = 169

→ s = √169

→ s = 13cm

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∴ Hence, Perpendicular height of the cone is 12cm & slant height of the cone 13cm.

Answer 2

Given:-

• The ratio of the radius of the base and height of the cone is 5:12.
• Its volume is 314m³.

To Find:-

• find its perpendicular height and slant height ?

step-by-step solution:-

• Let height of the cone be h.

Here,

• Base = Radius = 5x
• Height = Perpendicular = 12x
• Volume = 314m³

• Let radius of the cone be r.

⠀

To find perpendicular height(12x),

⟶ Volume of cone = 1/3 × πr²h

⟶ 314 = 1/3 × 22/7 × (5x)² × 12x

⟶ 314 = 1/3 × 3.14 × 25x² × 12x

⟶ 314 = 1 × 3.14 × 25x² × 4x

⟶ 3.14 × 100 x³ = 314

⟶ x³ = 1

⟶ x = 1

Therefore,

• Height = 12x = 12 × 1 = 12cm
• Radius = 5x = 5 × 1 = 5cm

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• To find slant height,

• Let slant height be l.

⟶ l² = h² + r²

⟶ l² = (12)² + (5)²

⟶ l² = 144 + 25

⟶ l² = 169

⟶ l = √169

⟶ l = 13cm

⠀⠀━━━━━━━━━━━━━━━━━━━⠀

∴ Hence , Perpendicular height of the cone is 12cm & slant height of the cone 13cm.