Question

A joker's cap is in the form of a right circular cone of base diameter 14 cm and height is 24cm. Find the area of the sheet required to make 11 such caps.​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Sheet\:required=6050\:cm^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Diameter \: of \: cone = 14 \: cm \\ \\ \tt: \implies Height \: of \: cone = 24 \: cm \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Area \: of \: sheet \: require \: to \: make \: 11 \: cap =?$

• According to given question :

$\tt \circ \: Radius = 7 \: cm \\ \\ \tt \circ \: Height = 24 \: cm \\ \\ \tt \circ \: l = \sqrt{ {r}^{2} + {h}^{2} } \\ \\ \tt: \implies l = \sqrt{ {7}^{2} + {24}^{2} } \\ \\ \tt: \implies l = \sqrt{49 +576 } \\ \\ \tt: \implies l = \sqrt{625} \\ \\ \tt: \implies l = 25 \: cm \\ \\ \bold{As \: we \: know \:that} \\ \tt: \implies C.S.A\: of \: cone = \pi rl \\ \\ \tt: \implies C.S.A \: of \: cone = \frac{22}{7} \times 7 \times 25 \\ \\ \tt: \implies C.S.A \: of \: cone =22 \times 25 \\ \\ \green{\tt: \implies C.S.A \: of \: cone =550 { \: cm}^{2} } \\ \\ \bold{For \: 11 \: caps : } \\ \tt: \implies Sheet \: required = 550 \times 11 \\ \\ \green{\tt: \implies Sheet \: required =6050 \: {cm}^{2} }$

Answer 2

$\huge\sf{Answer:}$

☆ According to the given question:

⇏ A joker's cap is in the form of a right circular cone of base diameter 14 cm and height is 24cm.

☆ Find:

⇏ Find the area of the sheet required to make 11 such caps.

☆ Know terms:

⇏ Length = (L)

⇏ Radius = (r)

⇏ Height = (h)

⇏ Curved surface area = (CSA)

☆ Using formula:

⇏ $\sf L = \sqrt{r^2 + h^2}$

☆ Calculations:

⇏ $\sf L = \sqrt{ 7^2 + 24^2}$

⇏ $\sf L = \sqrt{49 + 576}$

⇏ $\sf L = \sqrt{625}$

⇏ $\sf L = 25$

So, 25 is the length.

☆ Using formula:

⇏ $\sf CSA \: of \: cylinder = πrl$

☆ Using the above formula in our equation, we get:

⇏ $\sf CSA = \dfrac{22}{7} \times 7 \times 25$

⇏ $\sf CSA = (22 \times 25)$

⇏ ${\sf{\boxed{\sf{ CSA = 550 \: cm^2}}}}$

so, 550 cm² is the CSA of cone.

☆ Finding the area of required sheet:

⇏ $\sf 550 \times 11$

⇏ ${\sf{\boxed{\sf{6050 \: cm^2}}}}$

Therefore, 6050 cm² is the required area of sheet to make 11 caps.