Page 185 - Maths Skills - 8

Mensuration 183

22
Total surface area = 2πr (h + r) sq. units = 2 × × 14 × (21 + 14) cm 2
7
22
= 2 × × 14 × 35 cm = 3080 cm .
2
2
7
Example 3: How many cubic metres of earth must be dug out to sink a well which is 14 m deep and has a
diameter of 8 m? If the earth taken out is spread over a rectangular plot 16 m by 10 m, what is the
height of the platform so formed?
diameter 8 m
Solution: Here, h = 14 m and radius = = = 4 m.
2 2
22
The volume of the earth dug out = πr h = 7 × (4 m) × 14 m = 704 m 3
2
2
Area of the rectangular plot = length × breadth = 16 m × 10 m = 160 m 2
Volume of the platform formed = Volume of the earth taken out height of the platform formed
Volume 704 m 3
Thus, height = = = 4.4 m
Area 160 m 2
Hence, the height of the platform formed is 4.4 m.

Example 4: The volume of 7 m long circular iron tube is 1078 m . Find its diameter.
3
Solution: Here, length of iron tube = 7 m, i.e., h = 7 m and volume = 1078 m .
3
 πr h = 1078 m 3
2
1078 m 3 1078 × 7m 3
⇒ r = = = 49 m 2
2
πh 22 × 7 m
\ r = 7 m
\ Diameter = 2r = 2 × 7 m = 14 m.

Example 5: The curved surface area of a 12 m high cylinder is 200 m . Find the volume of the cylinder.
2
Solution: Here, curved surface area = 200 m and h = 12 m.
2
\ 2πrh = 200 m 2
200 m 2 100 m 25
r = 2π × 12 m = 12π = 3π m

25 25
Volume of the cylinder = πr h = π × × × 12 m = 265.15 m .
3
3
2
3π 3π
CHALLENGE

Complete the Following Table

Shape Dimensions C.S.A. T.S.A. Volume

Cube Side a Units a 3
Cuboid Length l Breadth b 2(lb + bh + lh)

Right Circular Cylinder Radius of Base = r, Height = h 2πrh πr h
2