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CBSE Class 9 Mathematics Question 7 of 44

Surface Areas and Volumes — Question 7

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Question

Question 7

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

Given,

Radius of conical cap (r) = 7 cm

Height of conical cap (h) = 24 cm

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. NCERT Class 9 Mathematics CBSE Solutions.

By formula,

Slant height of conical cap (l) = r2+h2\sqrt{r^2 + h^2}

Substituting values we get :

l=(7)2+(24)2=49+576=625=25 cm.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

= 227\dfrac{22}{7} × 7 × 25

= 38507\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.