Question

Please anyone tell me..with full explanation​

Answer 1

Question:

The circumference of the base of 16 m high solid cone is 33 m. Then find curved surface area of the cone.

Answer:

The curved surface area of the cone is 279.35 m² ( Approx. ).

Step-by-step-explanation:

We have given that,

Circumference of the base of cone = 33 m

Height of the cone = 16 m

We have to find the curved surface area of the cone.

Now, we know that,

Circumference of circular base = 2 π r

⇒ 33 = 2 * ( 22 / 7 ) * r

⇒ ( 33 * 7 ) / ( 2 * 22 ) = r

⇒ r = 33 ÷ 22 * 7 ÷ 2

⇒ r = 3 ÷ 2 * 3.5

⇒ r = 1.5 * 3.5

⇒ r = 5.25 m

Now, we know that,

( Slant height )² = ( Base radius )² + ( Height )²

⇒ l² = r² + h²

⇒ l² = ( 5.25 )² + ( 16 )²

⇒ l² = 27.5625 + 256

⇒ l² = 283.5625

⇒ l = √( 283.5625 ) - - [ Taking square roots ]

⇒ l = 16.928

⇒ l = 16.93 m ( Approx. )

Now, we know that,

Curved surface area of cone = π r l

⇒ CSAᶜᵒⁿᵉ = ( 22 / 7 ) * 5.25 * 16.93

⇒ CSAᶜᵒⁿᵉ = 22 * 5.25 ÷ 7 * 16.93

⇒ CSAᶜᵒⁿᵉ = 22 * 0.75 * 16.93

⇒ CSAᶜᵒⁿᵉ = 16.5 * 16.93

⇒ CSAᶜᵒⁿᵉ = 279.345

⇒ CSAᶜᵒⁿᵉ = 279.35 m² ( Approx. )

∴ The curved surface area of the cone is 279.35 m² ( Approx. ).