Question

A right circular cone of radius 3 cm, has a curved surface area of 47.1 cm^2. Find the volume of the cone. (Use π = 3.14)

Answer 1

hope it helps.......

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Given,

${\boxed{\sf\:{CSA\;of\;cone\;is\; 47.1\;cm^2}}}$  

Also,

$\textbf{\underline{Radius\;of\;Cone\;is\;3 cm}}$  

CSA of Cone = πrl

47.1 = πrl

47.1 = 3.14 × 3 × l

47.1 = 9.42 × l

$\rm \: \: \: \: \: \: \: \: \:=\dfrac{47.1}{9.42}=l$

5cm = l

Now,

Using formula

l² = h² + r²

(5)² = h² + (3)²

25 = h² + 9

25 - 9 = h²

16 = h²

√16 = h²

4cm = h

Now,

Volume of Cone

$\rm \: \: \: \: \: \: \: \: \:=\dfrac{1}{3}\times \pi r^2 h$

$\rm \: \: \: \: \: \: \: \: \:=\dfrac{1}{\cancel{3}}\times 3.14\times\cancel{3}\times 3\times 4$

= 3.14 × 3 × 4

= 37.68 cm³