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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
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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:
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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