Question

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

Answer 1

To Find :–

The Area of the sheet required to make 10 such caps.

Given :-

⠀⠀⠀$\bigstar$⠀Height of the cone = 24 cm

⠀⠀⠀$\bigstar$⠀Radius of the circle = 7 cm

We know :-

⠀⠀⠀Surface area of a right-circular cone :

$\underline{\boxed{\bf{TSA = \pi rl + \pi r^{2}}}}$

Where :-

• r = Radius of the cone.
• l = Slant height of the cone.

⠀⠀⠀Slant height of a right-circular cone :

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

Where :-

• l = Slant height
• r = Radius
• h = Height

Concept :-

According to the Question, we have to find the area required to make 10 caps.

So , first we have to find the total surface area of the cone.

But as we know that the area of a can be found only if the values of the radius and slant height is known.

So by the given information and the formula for slant height , we can find the required value.

Solution :-

To Find the TSA of the right-circular cone :-

$:\implies \large{\bf{TSA = \pi rl + \pi r^{2}}}$

$:\implies \underline{\bf{TSA = \pi r(\sqrt{r^{2} + h^{2}}) + \pi r^{2}}}\:\:\:[\because \bf{l = \sqrt{r^{2} + h^{2}}}] \\ \\ \\ :\implies \bf{TSA = \dfrac{22}{7} \times 7 \times (\sqrt{7^{2} + 24^{2}}) + \dfrac{22}{7} \times 7^{2}} \\ \\ \\ :\implies \bf{TSA = \dfrac{22}{7} \times 7 \times (\sqrt{49 + 576}) + \dfrac{22}{7} \times 7^{2}} \\ \\ \\ :\implies \bf{TSA = \dfrac{22}{7} \times 7 \times \sqrt{625} + \dfrac{22}{7} \times 7^{2}} \\ \\ \\ :\implies \bf{TSA = \dfrac{22}{7} \times 7 \times 25 + \dfrac{22}{7} \times 49} \\ \\ \\ :\implies \bf{TSA = \dfrac{22}{\not{7}} \times \not{7} \times 25 + 22 \times 7} \\ \\ \\ :\implies \bf{22 \times 25 + 22 \times 7} \\ \\ \\ :\implies \bf{TSA = 550 + 154} \\ \\ \\ :\implies \bf{TSA = 704} \\ \\ \\ \therefore \bf{Total\:Surface\:Area = 704\:cm^{2}}$

Hence, the surface area of the cone cap is 704 cm².

⠀ Area of the caps required to make 10 caps :-

Given :-

• Area = 704 cm²
• No. of caps = 10

A/c , the product of the area and the no. of caps will give us the area required to make 10 caps.

Area Required to make 10 caps :-

⠀⠀⠀⠀⠀⠀⠀= (10 × 704) cm²

⠀⠀⠀⠀⠀⠀⠀= 7040 cm²

Hence, the area required to make 10 caps is 7040 cm².

Answer 2

Answer:

GIVEN ,

RADIUS IS 7 CM

HEIGHT IS 24CM

FIND SLANT HEIGHT ( L ) = √r²+h²

= √49+567

= √625

= 25 cm

NOW ,

CURVED SURFACE AREA OF CAP =Πrl

= 22/7 × 7 × 25

= 550 cm ²

NOW ,

FIND 10 CAPS AREA ,

CURVED SURFACE AREA = 550×10

= 5500cm²

HENCE PROVED !!