Question

A cone has a base area of 20m square and a volume of 160m cube. Find the height of the cone.

Answer 1

AnswEr :

We are provided one cone whose base area is 20 m² and it's Volume is 160 m³ and we are asked to find the height of cone. But before going to find the height of cone we need to find the radius of the cone. So, first we will calculate the radius of the cone and then we will calculate the height of the cone. So, let's start :

• B A S E A R E A O F T H E C O N E :

↠ Base Area of cone = πr²

↠ 20 m² = πr²

↠ 20 = 22/7 × r²

↠ r² = 20 × (7/22)

↠ r² = 140/22 m

_______________________________

• V O L U M E O F T H E C O N E :

↠ Volume of cone = ⅓πr²h

↠ 160 m³ = ⅓ × 22/7 × 140/22 × h

↠ 160 = ⅓ × 20 × h

↠ 160/20 = ⅓ × h

↠ 16/2 = ⅓ × h

↠ 8 = ⅓ × h

↠ 8 × 3 = h

↠ h = 24 m

∴ The Height (h) of the cone is 24 m.

Answer 2

Answer:

Height of the cone = 24m

Step-by-step explanation:

Question:

A cone has a base area of 20m square and a volume of 160m cube. Find the height of the cone.

Given:

• A cone has a base area of 20m square
• Volume of cone = 160m

To find:

• Height of the cone

★ Formula Used :-

$\star\;\underline{\boxed{\sf{\pink{\pi\ r^2\ =\ \bf 20m}}}}$

$\star\;\underline{\boxed{\sf{\pink{\dfrac{1}{3} \pi\ r^2\ h\ =\ \bf 160m}}}}$

★ Solution :-

$\tt{\pi r^2 \:= \: 20}$

$\implies\tt{ r^2 \:= \: \dfrac{20}{\pi}}$

Also,

$\tt{\dfrac{1}{3} \pi r^2 \:h\:= \: 160}$

Substitute $\implies\tt{ r^2 \:= \: \dfrac{20}{\pi}}$ in the formula of volume of cone.

$\implies\tt{\dfrac{1}{3} \pi \times \dfrac{20}{\pi} \:h\:= \: 160}$

$\implies\tt{\dfrac{20h}{3} = 160}$

$\implies\tt{h = \dfrac{16\cancel0\: \times \: 3}{2\cancel0}}$

$\implies\tt{h = 8 \times 3}$

$\star\;\underline{\boxed{\sf{\pink{h =\ \bf 24m}}}}$

Hence, height of the cone = 24m