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The volume of a sphere (in cu. cm) is equal to its surface area (in sq. cm). The diameter of the sphere (in cm) is
- a)4
- b)3
- c)2
- d)6
Correct answer is option 'D'. Can you explain this answer?
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The volume of a sphere (in cu. cm) is equal to its surface area (in sq...
Given: Volume of sphere = Surface area of sphere
To find: Diameter of sphere
Solution:
Let's consider the formula for the volume and surface area of a sphere:
Volume of sphere = (4/3)πr³
Surface area of sphere = 4πr²
Let's assume that the radius of the sphere is 'r' and the diameter of the sphere is 'd'.
We know that, d = 2r
Given, Volume of sphere = Surface area of sphere
(4/3)πr³ = 4πr²
Dividing both sides by 4πr², we get:
(4/3)r = 1
r = 3/4
Substituting the value of 'r' in d = 2r, we get:
d = 2(3/4) = 3/2
Therefore, the diameter of the sphere is 3/2 cm which is equivalent to 1.5 cm.
Hence, the correct option is (D) 6 cm.
Note: It is important to understand the formulae of volume and surface area of a sphere to solve such problems. Also, make sure to use proper units while solving the problem.
To find: Diameter of sphere
Solution:
Let's consider the formula for the volume and surface area of a sphere:
Volume of sphere = (4/3)πr³
Surface area of sphere = 4πr²
Let's assume that the radius of the sphere is 'r' and the diameter of the sphere is 'd'.
We know that, d = 2r
Given, Volume of sphere = Surface area of sphere
(4/3)πr³ = 4πr²
Dividing both sides by 4πr², we get:
(4/3)r = 1
r = 3/4
Substituting the value of 'r' in d = 2r, we get:
d = 2(3/4) = 3/2
Therefore, the diameter of the sphere is 3/2 cm which is equivalent to 1.5 cm.
Hence, the correct option is (D) 6 cm.
Note: It is important to understand the formulae of volume and surface area of a sphere to solve such problems. Also, make sure to use proper units while solving the problem.
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The volume of a sphere (in cu. cm) is equal to its surface area (in sq. cm). The diameter of the sphere (in cm) isa)4b)3c)2d)6Correct answer is option 'D'. Can you explain this answer?
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