Long Questions
1. A hollow copper ball has an external diameter 9.6 cm and a thickness of 0.3 cm. If 1 cubic cm of copper weights 10 gm, find the weight of the ball.
2. A water tank is formed with the combination of cylinder and hemisphere. The total height of the tank is 24 m and base area is 616 sq. m. If the tank is filled with water at the rate of 65 paisa per litre, what is the total cost for the water? Find it.
3. A tent is right cylindrical in shape upto a height of 4 m and then its sphere is a right circular cone with a maximum height of 28 m above the ground and the diameter of the base is 14m. Find the cost of painting the inner surface of the tent at Rs. 4 per square metre, whose base has the diameter 14 metre.
4.. Prove that the angle at the semi circle is a right angle.
Answers
Given : A hollow copper ball has an external diameter 9.6 cm and a thickness of 0.3 cm.
1 cubic cm of copper weights 10 gm,
To find : the weight of the ball.
Solution:
external diameter 9.6 cm
=> external radius = 9.6/2 = 4.8 cm
thickness = 0.3cm
internal radius = 4.8 - 0.3 = 4.5 cm
Volume of copper = External Volume - internal Volume
Volume of sphere = (4/3)πR³
Volume of copper = (4/3)π(4.8³ - 4.5³)
= (4/3)π(19.467)
= 81.54 cm³
1 cm³ weigh = 10 gm
=> 81.54 cm³ weigh = 81.54 x 10 gm
=> 81.54 cm³ weigh = 815.4 gm
weight of the ball. = 815.4 gm
base area is 616 m²
=> πr² = 616
=> (22/7)r² = 616
=> r² = 14²
=> r = 14
radius = 14 m
Total Height = 24 m
Height of cylinder = 24 - 14 = 10 m
Volume of cylinder = πr²h
= 616 * 10
= 6,160 m³
Volume of hemisphere = (2/3)πr³
= (2/3)(22/7)14³
= 5,749.33 m³
Total Volume = 6,160+ 5,749.33
= 11,909.33 m³
1 m³ = 1000 litre
Water = 11,909.33 * 1000 litre
rate of 65 paisa per litre
Cost = 11,909.33 * 1000 * 65/100
=> Cost =77,41,066.67 Rs
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