Nakul was doing an experiment to find the radius r of a ball. For this he took a cylindrical containerwith radius R= 7cm and height 10cm. He filled the container almost half by water as shown in thefigure-1. Now he dropped the ball in to the container as in figure-2. He obserevd that in fig-2, the waterlevel in the container raised from P to Q i.e to 3.4 cmBased on the above information, answer the following questions :(i) What is the volume of the cylinder? 1M(ii) What is the approximate radius of the ball ? 2M(iii) What is the total surface area of the spherical ball?
Question
Nakul was doing an experiment to find the radius r of a ball. For this he took a cylindrical containerwith radius R= 7cm and height 10cm. He filled the container almost half by water as shown in thefigure-1. Now he dropped the ball in to the container as in figure-2. He obserevd that in fig-2, the waterlevel in the container raised from P to Q i.e to 3.4 cmBased on the above information, answer the following questions :(i) What is the volume of the cylinder? 1M(ii) What is the approximate radius of the ball ? 2M(iii) What is the total surface area of the spherical ball?
Solution
(i) The volume V of a cylinder is given by the formula V = πR²h, where R is the radius and h is the height. Substituting the given values, we get:
V = π * (7cm)² * 10cm = 1540π cubic cm.
(ii) The rise in water level when the ball is dropped into the cylinder corresponds to the volume of the ball. The volume V of a sphere is given by the formula V = 4/3πr³, where r is the radius. Setting this equal to the volume of the water displaced, we get:
4/3πr³ = π * (7cm)² * 3.4cm.
Solving for r, we get r ≈ 3.1cm.
(iii) The total surface area A of a sphere is given by the formula A = 4πr². Substituting the value of r we found, we get:
A = 4π * (3.1cm)² ≈ 120.68 square cm.
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