Question

The bright of the right aircular cylinder is 10cm and the radius of the base is 7 cm. Then the difference between the total suface area and the curved sofa oten is​

Answer 1

Appropriate Question:

The height of the right circular cylinder is 10cm and the radius of the base is 7 cm. Then the difference between the total suface area and the curved surface area is?

Answer:

308 cm²

Step-by-step explanation:

As per the provided information in the given question, we have :

• Height of the cylinder (h) = 10 cm
• Base radius (r) = 7 cm

We are asked to calculate the difference between the total suface area and the curved surface area.

In order to calculate the difference between the total suface area and the curved surface area, firstly we need to calculate the T.S.A and C.S.A of the cylinder separately.

★ T.S.A of the cylinder :

$\longrightarrow \sf{\quad {T.S.A_{(Cylinder)} = 2\pi r ( r + h) }}$

• r denotes base radius
• h denotes height

$\longrightarrow \sf{\quad {T.S.A_{(Cylinder)} = \Bigg [2\times \dfrac{22}{7} \times 7 ( 10+ 7) \Bigg ] \; cm^2 }}$

Simplifying and performing addition in the brackets.

$\longrightarrow \sf{\quad {T.S.A_{(Cylinder)} = \Bigg [2\times \dfrac{22}{7} \times 7 (17) \Bigg ] \; cm^2 }}$

Multiplying 17 with 7 and 2 with 22.

$\longrightarrow \sf{\quad {T.S.A_{(Cylinder)} = \Bigg [ \dfrac{44}{7} \times 119 \Bigg ] \; cm^2 }}$

Dividing 119 by 7.

$\longrightarrow \sf{\quad {T.S.A_{(Cylinder)} = \Bigg [ 44 \times 17 \Bigg ] \; cm^2 }}$

Multiplying 44 with 17.

$\longrightarrow \quad { \textbf{\textsf{T.S.A}}_{\textbf{\textsf{(Cylinder)}}} = \textbf{\textsf{ 748 }}\: \textbf{\textsf{cm}}^{\textbf{\textsf{2}} }}$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

★ C.S.A of the cylinder :

$\longrightarrow \sf{\quad {C.S.A_{(Cylinder)} = 2\pi rh }}$

• r denotes base radius
• h denotes height

$\longrightarrow \sf{\quad {C.S.A_{(Cylinder)} = \Bigg [2\times \dfrac{22}{7} \times 7\times 10 \Bigg ] \; cm^2 }}$

Dividing 7 by 7 and multiplying 2 with 22.

$\longrightarrow \sf{\quad {C.S.A_{(Cylinder)} = \Bigg [ 44 \times 1\times 10 \Bigg ] \; cm^2 }}$

Performing multiplication.

$\longrightarrow \quad { \textbf{\textsf{C.S.A}}_{\textbf{\textsf{(Cylinder)}}} = \textbf{\textsf{ 440 }}\: \textbf{\textsf{cm}}^{\textbf{\textsf{2}} }}$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

★ Difference between T.S.A and C.S.A :

$\longrightarrow \sf{\quad {Difference = T.S.A - C.S.A }}$

Substituting the values.

$\longrightarrow \sf{\quad {Difference = (748 - 440) \; cm^2 }}$

Performing subtraction.

$\longrightarrow \quad \underline{\boxed{ \textbf{\textsf{Difference}} = \textbf{\textsf{ 308 }}\: \textbf{\textsf{cm}}^{\textbf{\textsf{2}} }}}$

Therefore,

⠀⠀★ Required Answer = 308 cm²