## Some plastic balls of radius 1 cm were melted and cast into a tube. The thickness, length and outer radius of the tube were 2 cm, 90 cm and 30 cm respectively. How many balls were melted to make the tube ?

Given radius of plastic ball, r = 1cmThickness of tube = 2cmHeight of tube, h = 90cmOuter radius, R = 30cmInner radius of tube ,r1 = outer radius – thickness= 30-2 = 28cmVolume of plastic needed for tube = volume of outer tube – volume of inner tube= R2h -r12h= h(R2-r12)= ×90(302-282)= ×90(900-784)= ×90×116= 10440cm3Volume of […]

## A washing tub in the shape of a frustum of a cone has height 21 cm. The radii of the circular top and bottom are 20 cm and 15 cm respectively. What is the capacity of the tub ?( = 22/7)

Given r1 = 20cmr2 = 15cmHeight , h = 21cmVolume of frustum ,V = (1/3)h(r12+r22+r1×r2)V = (1/3)×(22/7)×21×(202+152+20×15)V = 22×(400+225+300)V = 22×925V = 22×925= 20350cm3= 20.34litres [∵ 1 litre = 1000cm3]Hence the capacity of the tub is 20.34 litres.

## Choose the correct alternative answer for each of the following questions.

(1) The ratio of circumference and area of a circle is 2:7. Find its circumference.(A) 14 (B) 7/ (C) 7 (D) 14/ Solution:Circumference of circle = 2rArea of circle = r2Given ratio of circumference and area = 2:72r/r2 = 2/72/r = 2/7r = 7cmCircumference = 2r = 2×7 = 14.Hence option A is the answer. (2) […]