Question

"Question 4 A conical tent is 10 m high and the radius of its base is 24 m. Find (i) slant height of the tent (ii) cost of the canvas required to make the tent, if the cost of 1 m^2 canvas is Rs 70.

Class 9 - Math - Surface Areas and Volumes Page 221"

Answer 1

given,
height ( h) = 10m
base radius (r) = 24m
(1) slant hight = √{height ² + radius ²}
= √{10² + 24²} = 26m

(ii) surface area of canvas = surface area of cone = πr× slant hight
= 22/7 × 24 × 26 m²

total cost of canvas for making = surface area of canvas × rate
= 22/7 × 24 × 26 × 70
= 22 × 24 × 26 × 10
= 137280 ₹

Answer 2

Right circular cone:

If a right angled triangle is revolved about one of the two sides forming a right angle keeping the other side fixed in position then the solid so obtained by segments is called right circular cone.

Slant height:

The length of the line segment joining the vertex to any point on a circular edge of the base is called the slant height of the cone.

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Given:

Radius of the base (r) = 24 m
Height of the conical tent (h) = 10 m

Let l be the slant height of the cone.

We know that
l²= r²+h²
 l = √h²+r²
 l = √10²+ 24²
l = √100 + 576
l = 26 m

Slant height (l)= 26 m

(ii) Canvas required to make the conical tent = Curved surface of the cone

Cost of 1 m2 canvas = ₹70

C.S.A of tent= πrl

= (22/7 × 24 × 26)

 = 13728/7 m²

∴ Cost of canvas = ₹ 13728/7 × 70 = ₹137280

Hence, required cost of the Canvas is  ₹137280

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Hope this will help you....