Page 298 - Start Up Mathematics_8 (Non CCE)

Example 38: How many circular coins each of radius 3.5 cm and 1.5 mm thickness should be melted to
form a cube of edge 5 cm? Write the answer to the nearest whole number.
Solution: Radius of coin (r) = 3.5 cm, Height of coin = 1.5 mm = 0.15 cm ( 1 cm = 10 mm)
2
2
Volume of 1 coin = pr h = p(3.5) (0.15) cm 3
22
3
= × 12.25 × 0.15 cm = 5.775 cm 3
7
3
3
Volume of cube = (Edge) = (5) = 125 cm 3
Let the number of coins be n.
n × Volume of 1 coin = Volume of cube
fi n × 5.775 = 125

125 125 1 000,¥
fi n = = = 21.65 ; 22
5 775. 5 775,
Hence, the number of coins is 22.

Example 39: A 11 cm × 4 cm rectangular sheet of paper is folded and taped without overlapping to make
a cylinder of height 4 cm. Find the volume of the cylinder so formed.

Solution:
11 cm
11 cm

4 cm 4 cm

Let the radius of the cylinder be r cm.
Height of cylinder (h) = 4 cm
Circumference of base = 2pr = 11 cm

22 711¥ 7
fi 2 × × r = 11 cm fi r = = cm
7 222¥ 4

7
2
3
3
\ Volume of cylinder = pr h = 22 Ê ˆ 2 ¥ 4 cm = 22 × 7 × 7 × 4 cm = 38.5 cm 3
¥
Á ˜
7 Ë 4¯ 7 4 4
Example 40: If the radius of the base of a right circular cylinder is halved keeping the height same, find
the ratio of the volume of the smaller cylinder to that of the original cylinder.
Solution: Original cylinder: Radius = r, Height = h
r
Smaller cylinder: Radius = , Height = h
2
Ê ˆ r 2 r 2
p Á ˜ h h
Volume of smallercylinder = Ë ¯ 2 = 4 = 1
2
Volume of original cylinder p rh r 2 4
\ The ratio of volume of smaller cylinder to that of original cylinder = 1 : 4

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