Question

The height of a cone is 16 cm and base radius is 12 cm. Find the curved surface area and the total surface area of the cone.(use π = 3.14)

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Answer 1

Given :

$\bullet\:\:\textsf{Height of the cone = \textbf{16 cm}}\\\bullet\:\:\textsf{Radius of the cone = \textbf{12 cm}}$

$\rule{130}1$

Solution :

let slant height of the cone be l.

➩ l² = h² + r²

➩ l² = 16² + 12²

➩ l² = 256 + 144

➩ l² = 400

➩ l = √400

➩ l = 20 cm

$\rule{170}2$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

→ CSA of cone = πrl

→ CSA of cone = 3.14 × 12 × 20

→ CSA of cone = 753.6 cm²

$\rule{130}1$

→ TSA of cone = πr (l + r)

→ TSA of cone = 3.14 × 12 (20 + 12)

→ TSA of cone = 3.14 × 12 (32)

→ TSA of cone = 1205.76 cm²

$\rule{170}2$

★ Therefore,

• CSA of cone is 753.6 cm².

• TSA of cone is 1205.76 cm².

Answer 2

Answer:

CSA of the cone is 753.6 cm² and the TSA of the cone is1205.76 cm².

Step-by-step explanation:

Given :-

• The height of a cone is 16 cm and the base radius is 12 cm.

To find :-

• The curved surface area and total surface area of the cone.

Solution :-

• Radius = 12 cm
• Height = 16 cm

Formula used :-

★ ${\boxed{\sf{CSA\:of\:cone=\pi\:rl}}}$

★ ${\boxed{\sf{TSA\:of\:cone=\pi\:r(r+l)}}}$

Now find the slant height (l) of the cone by using Pythagoras Theorem.

l² = r² + h²

→ l² = 12² + 16²

→ l² = 144 + 256

→ l² = 400

→ l = √400

→ l = 20

Slant height of the cone is 20 cm.

★ CSA of the cone ,

= πrl

= (3.14 × 12 × 20) cm²

= 753.6 cm²

Therefore, CSA of cone is 753.6 cm².

★ TSA of cone,

= πr(r+l)

= [3.14 × 12 (12+20) ] cm²

= (3.14 × 12 × 32) cm²

= 1205.76 cm²

Therefore, TSA of cone is 1205.76 cm².