Question

the volume of right circular cone is 9856cm³.If the radius of base 14 cm.find the----->
1. height of cone
2.Slant height​

Answer 1

$\underline{\underline{\sf{\maltese\:\:Question}}}$

The volume of right circular cone is 9856 cm³. If the radius of base 14 cm. Find the :

Height of Cone

Slant Height

$\underline{\underline{\sf{\maltese\:\:Given}}}$

The volume of right circular cone = 9856 cm³

Radius of Base = 14 cm

$\underline{\underline{\sf{\maltese\:\:To\:Find}}}$

Height of Cone

Slant Height

$\underline{\underline{\sf{\maltese\:\:Answer}}}$

Height of Cone = 48 cm

Slant Height of Cone = 50 cm

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

♣ First Let's Find Height of Cone

Volume of Right Circular Cone = 9856 cm³

⇒ 1/3πr²h = 9856 cm³

⇒ 1/3 × π × r² × h = 9856 cm³

⇒ 1/3 × 22/7 × r² × h = 9856 cm³ (∵ π = 22/7)

⇒ 22 × 1/7 × 3 × r² × h = 9856 cm³

⇒ 22/21 × r² × h = 9856 cm³

⇒ 22/21 × r² × h = 9856 cm³ (Given r = 14 cm)

⇒ 22/21 × (14 cm)² × h = 9856 cm³

⇒ 22/21 × 196 cm² × h = 9856 cm³

⇒ (22 × 196)/21 cm² × h = 9856 cm³

⇒ 4312/21 cm² × h = 9856 cm³

⇒ 616/3 cm² × h = 9856 cm³

Multiplying both sides by 3

⇒ 3 × (616/3) cm² × h = 3 × 9856 cm³

⇒ 616 cm² × h = 29568 cm³

Dividing both sides by 616 cm²

⇒ (616 cm² × h)/616 cm² = 29568 cm³/616 cm²

⇒ h = 29568/616 cm

⇒ h = 48 cm

∴ Height of Cone = 48 cm

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♣ Now Let's Find Slant Height

Slant Height = √(r² + h²)

⇒ Slant Height = √[(14 cm)² + h²] (Given r = 14 cm)

⇒ Slant Height = √[196 cm² + h²]

⇒ Slant Height = √[196 cm² + (48 cm)²] (We found : h = 48 cm)

⇒ Slant Height = √[196 cm² + 2304 cm²]

⇒ Slant Height = √[2500 cm²]

⇒ Slant Height = √[50² cm²]

⇒ Slant Height = √[50²] cm

⇒ Slant Height = 50 cm

∴ Slant Height of Cone = 50 cm

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Answer 2

height=48 cm

Slant Height =50 cm