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A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

Name: A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required
Uploaded: 2020-05-08T13:51:21Z
Duration: 3 min 37 s
Description: It is given that the heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. We have found that the volume of the conical heap is 86.625 m³ and the area of the canvas required is 99.759 m².

Solution:

Since the heap of wheat is in the form of a cone and the canvas required to cover the heap will be equal to the curved surface area of the cone.

Volume of a cone of base radius, 'r' and height, 'h' = 1/3πr²h

Curved surface area of the cone having a base radius, 'r' and slant height, 'l' = πrl

Slant height of the cone, l = √r² + h²

Diameter of the conical heap, d = 10.5 m

Radius of the conical heap, r = 10.5/2 m = 5.25 m

Height of the conical heap, h = 3 m

Volume of the conical heap = 1/3πr²h

= 1/3 × 22/7 × 5.25 m × 5.25 m × 3 m

= 86.625 m³

Slant height, l = √r² + h²

= √(5.25)² + (3)²

= √27.5625 + 9

= √36.5625

= 6.046 m (approx.)

The area of the canvas required to cover the heap of wheat = πrl

= 22/7 × 5.25 m × 6.046 m

= 99.759 m²

The volume of the conical heap is 86.625 m³ and the area of the canvas required is 99.759 m².

☛ Check: NCERT Solutions for Class 9 Maths Chapter 13

Video Solution:

A heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. Find its volume. The heap is to be covered by canvas to protect it from rain. Find the area of the canvas required.

NCERT Solutions for Class 9 Maths Chapter 13 Exercise 13.7 Question 9

Summary:

It is given that the heap of wheat is in the form of a cone whose diameter is 10.5 m and height is 3 m. We have found that the volume of the conical heap is 86.625 m³ and the area of the canvas required is 99.759 m².

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