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 m² canvas is ₹ 70.

Solution:

The total surface area of the cone is the sum of the curved surface area and area of the base which is a circle.

Curved surface area of a right circular cone of base radius, 'r' and slant height, 'l' is πrl

Slant height, l = √r² + h² where h is the height of the cone and r is the radius of the base.

i) Radius, r = 24 m

Height, h = 10 m

Slant height, l = √r² + h²

= √(24)² + (10)²

= √576 + 100

= √676 

= 26 m

ii) Curved surface area of the cone = πrl

= 22/7 × 24 m × 26 m

= 13728/7 m²

The cost of the canvas required to make the tent, at ₹ 70 per m^² = 70 × Curved surface area of the cone

= 13728/7 × 70

= ₹ 137280

Thus, slant height of the tent is 26 m and the cost of the canvas is ₹ 137280.

☛ Check: NCERT Solutions Class 9 Maths Chapter 13

Video Solution:

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 m² canvas is ₹ 70

Class 9 Maths NCERT Solutions Chapter 13 Exercise 13.3 Question 4

Summary:

It is given that there is a conical tent that is 10 m high and the radius of its base is 24 m. We have found that slant height of the tent is 26 m and the cost of the canvas to make the tent if the cost of 1 m² canvas is ₹ 70 is equal to ₹ 137280.

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