# A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on other. The radius and height of the cylindrical part are$5cm$ and$13cm$ respectively. The radii of hemisphere and conical parts are the same as that of the cylindrical part. Find the surface area of the toy if the total height of the conical part is$12cm$.

Answer

Verified

294.4k+ views

Hint: Calculate the surface area of all three shapes separately and later add. Use respective known formulas of surface area.

Now it is given that

Height of cylindrical part,$h$ $ = 13cm$

Radius of cylindrical part,$r$ $ = 5cm$

The radii of the spherical part and base of the conical part are also $r$.Let us suppose ${h_1}$ be the height of the conical part and $l$ be the slant height of the conical part.

We Know that,

$

{l^2} = {r^2} + {h_1}^2 \\

\Rightarrow l = \sqrt {{r^2} + {h_1}^2} \\

\Rightarrow l = \sqrt {{5^2} + {{12}^2}} = 13cm \\

$

Now, the surface area of the toy$ = $ curved surface area of the cylindrical part$ + $ curved surface area of the hemispherical part$ + $ curved surface area of the conical part.

$

= \left( {2\pi rh + 2\pi {r^2} + \pi rl} \right)c{m^2} \\

= \pi r\left( {2h + 2r + l} \right)c{m^2} \\

= \left( {\dfrac{{22}}{7} \times 5 \times \left( {2 \times 13 + 2 \times 5 + 13} \right)} \right)c{m^2} \\

= 770c{m^2} \\

$

Therefore, the surface area of the toy$ = 770c{m^2}$

Note- Whenever we face such types of questions the key concept is that we should write what is given to us and then use the formula that is suitable according to the question, like we did. Here, we find the slant height, the slant height of the cone and then knowing the values of curved surface area of the cylindrical part, curved surface area of the hemispherical part and curved surface area of the conical part we get our answer.

Now it is given that

Height of cylindrical part,$h$ $ = 13cm$

Radius of cylindrical part,$r$ $ = 5cm$

The radii of the spherical part and base of the conical part are also $r$.Let us suppose ${h_1}$ be the height of the conical part and $l$ be the slant height of the conical part.

We Know that,

$

{l^2} = {r^2} + {h_1}^2 \\

\Rightarrow l = \sqrt {{r^2} + {h_1}^2} \\

\Rightarrow l = \sqrt {{5^2} + {{12}^2}} = 13cm \\

$

Now, the surface area of the toy$ = $ curved surface area of the cylindrical part$ + $ curved surface area of the hemispherical part$ + $ curved surface area of the conical part.

$

= \left( {2\pi rh + 2\pi {r^2} + \pi rl} \right)c{m^2} \\

= \pi r\left( {2h + 2r + l} \right)c{m^2} \\

= \left( {\dfrac{{22}}{7} \times 5 \times \left( {2 \times 13 + 2 \times 5 + 13} \right)} \right)c{m^2} \\

= 770c{m^2} \\

$

Therefore, the surface area of the toy$ = 770c{m^2}$

Note- Whenever we face such types of questions the key concept is that we should write what is given to us and then use the formula that is suitable according to the question, like we did. Here, we find the slant height, the slant height of the cone and then knowing the values of curved surface area of the cylindrical part, curved surface area of the hemispherical part and curved surface area of the conical part we get our answer.

Recently Updated Pages

Which of the following would not be a valid reason class 11 biology CBSE

What is meant by monosporic development of female class 11 biology CBSE

Draw labelled diagram of the following i Gram seed class 11 biology CBSE

Explain with the suitable examples the different types class 11 biology CBSE

How is pinnately compound leaf different from palmately class 11 biology CBSE

Match the following Column I Column I A Chlamydomonas class 11 biology CBSE

Trending doubts

Which of the following Chief Justice of India has acted class 10 social science CBSE

Green glands are excretory organs of A Crustaceans class 11 biology CBSE

What if photosynthesis does not occur in plants class 11 biology CBSE

What is 1 divided by 0 class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

10 slogans on organ donation class 8 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is the past tense of read class 10 english CBSE