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Mathematics

The area of the base of a conical solid is 38.5 cm2 and its volume is 154 cm3. Find the curved surface area of the solid.

Mensuration

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Answer

Given,

Area of the base of conical solid = 38.5 cm2

⇒ πr2 = 38.5 …………(1)

⇒ 227r2\dfrac{22}{7}r^2 = 38.5

⇒ r2 = 38.5×722\dfrac{38.5 \times 7}{22} = 12.25

⇒ r = 12.25\sqrt{12.25} = 3.5 cm

Given,

⇒Volume =154⇒13πr2h=154⇒13×38.5×h=154[From (1)]⇒h=154×338.5⇒h=12 cm.\Rightarrow \text{Volume } = 154 \\[1em] \Rightarrow \dfrac{1}{3}πr^2h = 154 \\[1em] \Rightarrow \dfrac{1}{3} \times 38.5 \times h = 154 \quad [\text{From (1)}] \\[1em] \Rightarrow h = \dfrac{154 \times 3}{38.5} \\[1em] \Rightarrow h = 12 \text{ cm}.

By formula,

⇒ l2 = r2 + h2

⇒ l2 = (3.5)2 + (12)2

⇒ l2 = 12.25 + 144

⇒ l2 = 156.25

⇒ l = 156.25\sqrt{156.25} = 12.5 cm.

Curved surface area = πrl

= 227×3.5×12.5\dfrac{22}{7} \times 3.5 \times 12.5

= 137.5 cm2.

Hence, curved surface area = 137.5 cm2.

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