Question

The Volume of a cylinder is 448 π cm 3 and height 7 cm. Find its total surface area. (754.28cm 2 )

Answer 1

Given :

• Volume of cylinder = 448π cm³
• Height = 7cm

To find :

TSA of cylinder

Formula used :

• Volume of cylinder = πr²h
• TSA of cylinder = 2πr(h + r)

Solution :

First of all we will find radius of base of cylinder

$\sf \implies \: Volume \: = \pi \times {r}^{2} \times h \\ \\ \sf \implies \: 448\pi \: {cm}^{3} = \pi \times {r}^{2} \times 7cm \\ \\ \sf \implies \: {r}^{2} \: = \: \dfrac{448\pi \: {cm}^{3} }{\pi \times 7cm} \\ \\ \sf \implies \: {r}^{2} = \dfrac{448 \: {cm}^{2} }{7} \\ \\ \sf \implies \: {r}^{2} \: = \: 64 {cm}^{2} \\ \\ \sf \implies \: r \: = \: \sqrt{64 \: {cm}^{2} } \sf \implies \:r \: = \: \pm \: 8cm \\ \\ \sf \: as \: side \: cannot \: be \: negative \: \\ \sf \implies \:r \: = \: + 8cm$

Now ,

Height = 7cm

Radius = 8cm

$\sf \implies \: TSA \: = \:2\pi \: r(r + h) \\ \\ \sf \implies \: TSA \: = \:2\pi \times 8cm \times (8 cm + 7cm) \\ \\ \sf \implies \: TSA \: = \:2 \times \pi\times 8 \times 15 \: {cm}^{2} \\ \\ \sf \implies \: TSA \: = \:240\pi \: {cm}^{2} \\ \\ \sf \implies \: TSA \: = \:240 \times 3.14 \: {cm}^{2} \\ \\ \sf \implies \: TSA \: = \:753.6\: {cm}^{2}$

ANSWER : 753.6 cm²

Answer 2

Answer:

Total surface area = 240π cm2