Question

The area of the base of a right circular cone is 154 sq. cm and its height is 24 cm, then its curved
surface area is
​

Answer 1

Area of base = 154

=> πr^2 = 154

=> (22/7)*r*r = 154

=> r*r = 154*7/22

=> r = √ 7*7

.•. r = 7 cm

h = 24 cm

l = √((24*24)+(7*7))

= √(576+49)

= √625

= 25 cm

Curved Surface Area = πrl = (22/7)*7*25 = 550 cm^2

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Answer 2

Answer :-

Curved surface area is 550 cm².

Explanation :-

Area of the base of a right circular cone = 154 cm²

Base of the right circular cone is circle

⇒ πr² = 154 cm²

⇒ (22/7) * r² = 154

⇒ r² = 154 * (7/22)

⇒ r² = 7 * 7

⇒ r² = 7²

⇒ r = 7

Radius of the base of the right circular cone = 7 cm

Height of the right circular cone (h) = 24 cm

Let the slant height if the right circular cylinder be 'l' cm

We know that

l² = h² + r²

⇒ l² = (24)² + (7)²

⇒ l² = 576 + 49

⇒ l² = 625

⇒ l² = 25²

⇒ l = 25

Slant height (l) = 25 cm

We know that

Curved surface area of the right circular cone = πrl

= (22/7) * 7 * 25

= 22 * 1 * 25

= 22 * 25

= 550

∴ curved surface area is 550 cm²