Question

If a right circular cone has radius 4 cm and slant height 5 cm then what is its volume? options a) 16 π cm3 b) 14 π cm3 c) 12 π cm3 d) 18 π cm3

Answer 1

$\huge\underline\mathbb{\red A\pink{N}\purple{S} \blue{W} \orange{E}\green{R :}}$

★ Given that,

Find the Volume of Cone whose radius and height are :

$\tt\:◼ \: Radius_{(Cone)} = 4cm$

$\tt\: ◼ \: Slant \: Height_{(Cone)} = 5 cm$

$\tt\: ◼ \: Height_{(Cone)} = ?$

To find the Height of cone. Use the formula of Slant height.

$\tt\purple{ ◼ \: Slant \: height = l² = h² + r²}$

• Substitute the values.

$\tt\:⟹(5)² = h² + (4)²$

$\tt\:⟹25 = h² + 16$

$\tt\:⟹h² = 25 - 16$

$\tt\:⟹h² = 9$

$\tt\:⟹ h = \sqrt{9}$

$\tt\:⟹h = 3$

$\boxed{\bf{\purple{∴ Height\:of \: cone=3cm}}}$

$\tt\:⟹Volume \: of \: cone = \frac{1}{3}\timesπ {r}^{2} h$

$\tt\:⟹\frac{1}{3}\timesπ\times{4}^{2}\times3</p><p>$

$\tt\:⟹16π$

$\underline{\boxed{\bf{\blue{∴ The \: Volume \: of \: Cone \: = 16π{cm}^{3}}}}}</p><p>$

Answer 2

Radius = 4cm

Slant Height ( l) = 5cm

Height = ?

we know that ,

Slant Height =

${l}^{2} = {h}^{2} + {r}^{2}$

${5}^{2} = {h}^{2} + {4}^{2}$

$25 = {h}^{2} + 16$

${h}^{2} = 25 - 16$

${h}^{2} = 9$

$h = \sqrt{9}$

$h = 3$

$volume \: of \: cone = \frac{1}{3} \times \pi {r}^{2} h$

$\frac{1}{3} \times \pi \times {4}^{2} \times 3$

$= 16\pi {cm}^{3}$

Step-by-step explanation:

I hope it helps u dear friend ^_^♡♡