Question

if a cylinder has curved surface area of 72cm² and radius of 4cm find its height amd Total surface area​

Answer 1

Given :

• CSA of cylinder = 72 cm²
• Radius of base of cylinder = 4cm

To find :

• Height of cylinder
• TSA of cylinder

Formula used :

• CSA of cylinder = 2πrh
• TSA of cylinder = 2πrh + 2πr²

Solution :

First of all we will find height by using formula for CSA.

$\sf \implies 72cm^2 = 2\pi \times 4cm \times h$

$\sf \implies \: h \: = \: \dfrac{72cm^2 }{2\pi \times 4cm }$

$\sf \implies \: h \: = \: \dfrac{72cm^2 }{8\pi cm }$

$\sf \implies \: h \: = \: \dfrac{9cm }{\pi }$

$\sf \implies \: h \: = \: \dfrac{9 \: cm}{3.14 }$

$\sf \implies \: h \: = \: \: 2.87 \: cm$

________________________________

➝ TSA = 2πrh + 2πr²

➩ TSA = 2πr(h+r)

➩ TSA = 2 × 3.14 × 4cm × ( 2.87cm + 4cm )

➩ TSA = 8 × 3.14 cm × 6.87 cm

➩ TSA = 172.574 cm²

________________________________

ANSWER :

• Height = 2.87 cm
• TSA = 172.574 cm²