Mathematics

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.

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Given,

Radius of conical cap (r) = 7 cm

Height of conical cap (h) = 24 cm

By formula,

Slant height of conical cap (l) = $\sqrt{r^2 + h^2}$

Substituting values we get :

$l = \sqrt{(7)^2 + (24)^2} \\[1em] = \sqrt{49 + 576} \\[1em] = \sqrt{625} = 25 \text{ cm}.$

By formula,

Curved surface area of one conical cap = πrl

= $\dfrac{22}{7}$ × 7 × 25

= $\dfrac{3850}{7}$

= 550 cm²

Curved surface area of 10 such conical caps = 10 × 550 cm² = 5500 cm².

Hence, area of sheet required for making 10 caps = 5500 cm².

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