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RS Aggarwal Solutions Class 9 Mathematics Solutions for Volume And Surface Area Of Solids Exercise 15C in Chapter 15 - Volume And Surface Area Of Solids

Question 11 Volume And Surface Area Of Solids Exercise 15C

A heap of wheat is in the form of a cone of diameter 9m and height 3.5m. Find its volume. How much canvas cloth is required to just cover the heap? (Use π = 3.14.)

Answer:

ANSWER:

It is given that

The diameter of the conical heap = 9m

Radius of the conical heap = 9/2 = 4.5m

Height of the conical heap = 3.5m

We know that

The volume of the conical heap = 1/3 πr2h

By substituting the values

The volume of the conical heap = 1/3 × 3.14 × 4.52 × 3.5

On further calculation

The volume of the conical heap = 3.14 × 1.5 × 4.5 × 3.5

So we get

The volume of the conical heap = 74.1825 m3

We know that

Slant height l =√ (r2 + h2)

By substituting the values

l = √ (4.52 + 3.52)

On further calculation

l = √ 32.5

So we get

l = 5.7 m

We know that

The curved surface area of the conical heap = πrl

By substituting the values

The curved surface area of the conical heap = 3.14 × 4.5 × 5.7

On further calculation

The curved surface area of the conical heap = 80.54 m2

Therefore, 80.54 m2 of the canvas is required to cover the heap of wheat.

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