Question

A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps​

Answer 1

Given :-

A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm.

To Find :-

Area of the sheet required to make 10 such caps​

Solution :-

We know that

${\large{\underbrace{\underline{\bf l^2=r^2+h^2}}}}$

$\rm\implies l^2=(7)^2+(24)^2$

$\rm\implies l^2=49+576$

$\rm\implies l^2=625$

$\rm\implies l=\sqrt{625}$

$\rm\implies l=25\;cm$

Now

Area of one cap = CSA of cone

We know that

${\large{\underbrace{\underline{\bf CSA\;of\;cone=\pi rl}}}}$

$\rm\implies CSA=\dfrac{22}{7}\times7\times25$

$\rm\implies CSA=22\times 25$

$\rm\implies CSA=550\;cm^2$

Now

${\underbrace{\underline{\bf Area \;of\; 10 \;caps = CSA \times 10}}}$

$\rm\implies Area=550\times10$

$\rm\implies Area=5500\;cm^2$

∴ Area of 10 such caps is 5500 cm²

Answer 2

Answer:

Area of sheet required to make 10 caps = 2512$cm^{2}$

Step-by-step explanation:

According to the information provided in the question it is given as

Joker cap in the form of  circular cone

Radius =7 cm

Height =24 cm

We need to find the area of sheet required to make 10 such cap

Here we find the area of cone

$A= \pi r(r+\sqrt{h^{2} } +r^{2}$

Putting the value we get the area

$A=\frac{22}{7}\times7(7+\sqrt{7^{2} }+24^{2})$

$A =\frac{22}{7} \times (49+ 7+24)\\A = \frac{22}{7}\times (80)\\A= 3.14\times 80\\A =251.2cm^{2}$

Now this is the area of one cone= area of one cap

 we need area of 10 caps= 251.2 x 10

                                           =2512$cm^{2}$

Hence Area of sheet required to make 10 caps = 2512$cm^{2}$