Question

Find the curved surface area of cone if radias of height are in the ratio of 4 : 3 and volume is 2156 cm

Answer 1

Hi,

Here is your answer,

Let the radius be 4a 

Height = 3a 

Volume = 2156

→ π ×r² × h / 3= 2156

→ 22×16a² × 3a / 7×3 = 2156

→ a³ × 22×16 = 2156 × 7

→ a³ = 2156×7/22×16

→ a³ = 49×7/8

→ a³ = 7×7×7/2×2×2

→ a = 7/2

Radius = 14 cm

Height = 10.5 cm

L = sqrt ( 196 + 110.25) 

L = sqrt ( 306.25)

.C.S.A= π×r L

→ 22×14 × 17.5 / 7

→ 44 ×17.5

→ 770 cm²

L = 17.5 cm


Hope it helps you !

Answer 2

Step-by-step explanation:

Let the radius be 4x and height be 3x of the right circular cone.

We have,

Area of the right circular cone = 2156 cm³

★ According to Question now,

➨ Volume of cone = ⅓ πr²h

➳ 2156 = 1/3 × 22/7 × (4x)² × (3x)

➳ 2156 = 1/3 × 22/7 × 16x² × 3x

➳ 2156 = 22/7 × 16x² × x

➳ 16x³ = 2156 × 7/22

➳ x³ = 98 × 7/16

➳ x³ = 7 × 7 × 7/2 × 2 × 2

➳ x = 7/2

➳ x = 3.5 cm

Therefore,

Radius = 4x = 4(3.5) = 14 cm

Height = 3x = 3(3.5) = 10.5 cm

______________________

➳ Slant height (l)² = r² + h²

➳ l² = (14)² + (3.5)²

➳ l² = 196 + 110.25

➳ l² = 306.25

➳ l = √306.25

➳ Slant Height (l) = 17.5 cm

_____________________

➳ CSA of cone = πrl

➳ CSA of cone = 22/7 × 14 × 10.5

➳ CSA of cone = 22 × 2 × 10.5

➳ CSA of cone = 44 × 10.5

➳ CSA of cone = 770 cm²