Question

A jokers cap is in the form of a right circular cone of base radius 5 cm and height 12 cm find the area of the sheet required to make 15 such caps

Answer 1

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Answer 2

$\huge{\underline{\underline{\mathrm{\orange{GIVEN:-}}}}}$

• The height of the circular cone cap is 12 cm
• The base radius of circular cone 5 cm

$\huge{\underline{\underline{\mathrm{\orange{TO\:FIND:-}}}}}$

Find the area of sheet required to make 15 caps = ?

$\huge{\underline{\underline{\mathrm{\orange{FORMULA \:USED:-}}}}}$

$\large{\boxed{\bf{\red{C.S.A.\: of\: cone = πrl}}}}$

$\huge{\underline{\underline{\mathrm{\orange{SOLUTION:-}}}}}$

To find the C.S.A. of cone , we need to find the slant height of the cone

we know that, the formula to find the slant height of the cone is :- $\bf{l = \sqrt{{h}^{2} + {r}^{2}}}$

putting the values in formula,we get

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

$\implies$$\bf{ l = \sqrt{{(12)}^{2} + {(5)}^{2}}}$

$\implies$$\bf{ l = \sqrt{144 + 25}}$

$\implies$$\bf{ l = \sqrt{169}}$

$\implies$$\bf{ l = \sqrt{13}\:cm}$

Now, we have to find the C.S.A. of cone

Put the values in the formula

$\implies$$\large\bf{ C.S.A. = πrl}$

Take π = $\bf{\frac{22}{7}}$

$\implies$$\bf{ C.S.A. = \frac{22}{7}\times 5 \times 13}$

$\implies$$\bf{ C.S.A. = \frac{110}{7}\times 13}$

$\implies$$\bf{ C.S.A. =\cancel \dfrac{1430}{7}}$

$\implies$$\large\bf\red{ C.S.A. = 204.28\: {cm}^{2}}$

The area of the sheet required to make 15 such caps is :-

$\longrightarrow$$\bf{ 204.28 \times 15}$

$\longrightarrow$$\large\bf\red{ 3064.2\: {cm}^{2}}$

Thus, the area of sheets required for 15 cones is 3064.2 cm²

$\large{\underline{\underline{\mathrm{\orange{FINAL\:ANSWER:-}}}}}$

$\huge{\boxed{\boxed{\bf{\red{C.S.A. = 3064.2\:{cm}^{2}}}}}}$