Question

volume of 15cm high right circular is 960π cm cube find the total surface area of the cylinder.​

Answer 1

Given -

$Volume \: of \: cylinder = 960\pi \: {cm}^{3}$

$height(h) \: of \: \: cylinder = 15 \: cm$

To find -

• Total surface area of cylinder

Solution -

We know that,

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

By putting the values we will get -

$960\pi = \pi {r}^{2} 15$

$\frac{960\pi}{15\pi} = {r}^{2}$

${r}^{2} = 64$

$r = \sqrt{64}$

$r = 8$

Radius (r) of the cylinder is 8 cm

Now,

$T. S. A\: of \: cylinder = 2\pi \: r(r + h)$

$T. S. A\: of \: cylinder = 2 \times \frac{22}{7} \times 8(8 + 15)$

$T. S. A\: of \: cylinder = \frac{8096}{7}$

$T. S. A\: of \: cylinder = 1156.57$

Therefore total surface area of the cylinder is 1156.57 cm²