Question

The volume of a cylinder is 38016 cm3 and its height is 21 cm. What is its
curved surface area?​

Answer 1

$\huge\bf\green{AnsWeR:-}$

$\underline{\underline{\tt{Radius = 24cm} }}$

$\underline{\underline{\tt{Curved\:surface\:area\:of \: cylinder = 3168{cm}^{3} } }}$

$\huge\tt\red{SoLutIon}$

Given that :-

☞ Height = 21cm

☞ Volume of a cylinder = 38016cm³

Find out :-

☞ Radius

☞ Curved surface area

Then according to the question:-

using formula,

$\huge{\boxed{\pink{ Volume\: of \:cylinder\: = \pi{r}^{2}h } }}$

➜ 38016 = πr²h

➜ 38016 = 22/7 × r² × 21

➜ r² = 38016× 7 /22 × 21

➜ r² = 12672/22

➜ r² = 576

➜ r = 24 cm

Therefore,

using formula,

$\huge{\boxed{\pink{ Curved\: surface \: area\: of \: cylinder = 2\pi rh} }}$

Curved surface area of cylinder = 2 × 22/7 × 24 × 21

Curved surface area of cylinder = 2 × 22 × 24 × 3

Curved surface area of cylinder = 3168cm²