Question

The volume of a cylinder is 150 cm and height is 6 cm. Find the areas of it's total surface and (lateral) curved surface.​

Answer 1

$\large{\underline{\sf{\red{Required\:Answer:}}}}$

• $\large\boxed{\underline{{\sf 188.57 \: cm ^{2}}}}$

Given:-

• The volume of cylinder = $\sf{ 150\pi cm^{3}}$

• Height of cylinder = 6 cm.

To Find:-

• Find it's TSA (total surface area) and LSA (lateral surface area).

Solution:-

• Let the radius of cylinder be r cm.

We know that,

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

$\pink{\implies\:\:}$ ${\sf{ 150\pi = \pi r^{2}h }}$

$\pink{\implies\:\:}$ ${\sf{ \dfrac{150\pi}{\pi} = r ^{2} (6)}}$

$\pink{\implies\:\:}$ ${\sf{\dfrac{150}{6} = r ^{2} }}$

$\pink{\implies\:\:}$ ${\sf{ 25 = {r}^{2} }}$

$\pink{\implies\:\:}$ ${\sf{ \sqrt{25} = {r}}}$

$\pink{\implies\:\:}$ ${\sf{ 5 = {r}}}$

So, the radius of the cylinder = 5 cm.

• ${\boxed{\red{\sf{ \:TSA = 2\pi r(h + r)}}}}$

$\purple{\implies\:\:}$ ${\sf{TSA = 2( \frac{22}{7} )(5)(6 + 5)}}$

$\purple{\implies\:\:}$ ${\sf{ \dfrac{44}{7} (5)(11)}}$

$\purple{\implies\:\:}$ ${\sf{ \dfrac{44}{7} (55)}}$

$\purple{\implies\:\:}$ ${\sf{ 345.71 \: {cm}^{2} }}$

• ${\boxed{\red{\sf{ \:LSA = 2\pi rh }}}}$

$\blue{\implies\:\:}$ ${\sf{LSA = 2( \dfrac{22}{7} )(5)(6)}}$

$\blue{\implies\:\:}$ ${\sf{ \dfrac{44}{7} (30)}}$

$\blue{\implies\:\:}$ ${\sf{ \dfrac{1320}{7} }}$

$\blue{\implies\:\:}$ ${\sf{188.57 \: cm ^{2} }}$

Answer 2

volume of cylinder =150 pi cu.cm

height of cylinder =6 cm

volume of cylinder =pi r^2 h

pi r^2 h =150 pi

r^2 (6)=150

r^2 =25

r=5

surface area =2pi r (r+h)

                   =2pi (5)(5+6)

                    =2pi(5)(11)

                     =2pi x 55

                     =110 pi

lateral surface area =2 pi rh

                               2 pi (5)(6)

                              =2pi(30)

                              =60 pi