Question

7. The curved surface area of a cone is 1159 5/7cm². Area of its base is 254 4/7 cm2. Find its volume.

Answer 1

Answer:

3394 2/7 cm³

Step-by-step explanation:

Given :

CSA of a cone = 1159 $\frac{5}{7}$ cm²

Area of the base of the cone = 254 $\frac{4}{7}$ cm²

Assuming it is a right circular cone,

Procedure :

πrl = 1159 5/7 cm²

πr² = 254 4/7

Assuming π = 22/7,

(22/7)(r²) = 1782/7 [Circular base]

⇒ r² = 81 cm²

∴ r = +9 cm [Length cannot be negative]

Substituting r value in πrl,

(22/7)(9)(l) = 8118/7

⇒ l = 8118/(22 × 9)

∴ l = 41 cm

∴ Volume of the cone = (1/3)(πr²)(h)

h = $\sqrt{l^{2} - r^{2} }$

[∵ l (slant height) = r² + h²]

⇒ h = $\sqrt{41^{2} - 9^{2} }$

⇒ h = $\sqrt{1681 - 81}$

⇒ h = √1600

∴ h = 40 cm

Again, Volume of the cone = (1/3)(πr²)(h),

∴ Volume = (1/3)(1782/7)(40) cm³

⇒ Volume = (594/7)(40) cm³

⇒ Volume = 23760/7 cm³ (OR)

∴ Volume = 3394 2/7 cm³

Hoping that I have not made any mistakes, You're welcome.

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GeniusH