Question

A solid cylindrical shape whose radius is 5 cm
and hight is 21 cm. Find the curved surface
area and the whole surface area.​

Answer 1

Curved surface area=pi*r*h=3.14*5*21=329.7
Whole surface area=pi*r*h +pi*r*r=329.7+78.5=408.2

Answer 2

Answer :

• Curved surface area is 660 cm².

• Total Surface Area is 817.14 cm².

Clarification :

Here, we are given that the radius of the solid cylinderical shape is 5 cm & height is 21 cm. We have to find curved surface area and total surface area or whole surface area. So, basically we have to plug the values in the required formula given below :-

$\boxed{\begin{array}{cc} \star \: { \pmb{\blue{ {C.S.A}_{(Cylinder)} = 2 \pi rh} }} \\ \\ \star \: \: \pmb{\blue{ {T.S.A}_{(Cylinder)} = 2 \pi r(r+h) }} \end{array}}$

By substituting the values in the given formula, we'll find our answer.

Given :

• Radius (r) = 5 cm

• Height (h) = 21 cm

To calculate :

• Curved Surface Area

• Total Surface Area

Curved Surface Area :

We know,

$\star \: \: \boxed{\: { \pmb{\blue{ {C.S.A}_{(Cylinder)} = 2 \pi rh} }}} \\ \\ \\ \sf{ \longrightarrow \: {C.S.A}_{(Cylinder)} = 2 \times \dfrac{22}{7} \times 5 \times 21 } \\ \\ \\ \sf{ \longrightarrow \: {C.S.A}_{(Cylinder)} = 2 \times 22 \times 5 \times 3 } \\ \\ \\ \sf{ \longrightarrow \: {C.S.A}_{(Cylinder)} = 44 \times 15 } \\ \\ \\ \longrightarrow \underline{\boxed{\mathit \blue{ {C.S.A}_{(Cylinder)} = 660 \: {cm}^{2} }}} \: \blue{\bigstar}$

Henceforth, C.S.A of the cylinder is 660 sq. cm.

Total Surface Area :

$\star \: \: \boxed{\: { \pmb{\blue{ {T.S.A}_{(Cylinder)} = 2 \pi r(r + h)} }}} \\ \\ \\ \sf{ \longrightarrow \: {T.S.A}_{(Cylinder)} = 2 \pi rh + 2 \pi {r}^{2} } \\ \\ \\ \sf{ \longrightarrow \: {T.S.A}_{(Cylinder)} =660 + 2 \pi {r}^{2} } \\ \\ \bf(as \: 2 \pi rh = c.s.a) \\ \\ \\ \sf{ \longrightarrow \: {T.S.A}_{(Cylinder)} =660 + (2) \times \dfrac{22}{7} \times {5}^{2} } \\ \\ \\ \sf{ \longrightarrow \: {T.S.A}_{(Cylinder)} =660 + (2) \times \dfrac{22}{7} \times 25 } \\ \\ \\ \sf{ \longrightarrow \: {T.S.A}_{(Cylinder)} =660 + \bigg( \dfrac{ 2\times 22 \times 25}{7} \bigg) } \\ \\ \\ \sf{ \longrightarrow \: {T.S.A}_{(Cylinder)} =660 + \bigg( \dfrac{ 1100}{7} \bigg) } \\ \\ \\ \sf{ \longrightarrow \: {T.S.A}_{(Cylinder)} =660 + 157.14} \\ \\ \longrightarrow \underline{\boxed{\mathit \blue{{T.S.A}_{(Cylinder)} = 817.14 \: {cm}^{2} }}} \: \blue{\bigstar}$

Henceforth, whole surface area is 817.14 sq. cm.

Note : CSA and TSA are always calculated in square units.