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Find the ratio of the volume of a sphere of radius 4cm, to that of a sphere of radius 6 cm ?
- a)16:36
- b)27:8
- c)8:27
- d)36:16
Correct answer is option 'C'. Can you explain this answer?
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To find the ratio of the volume of a sphere of radius 4 cm to that of a sphere of radius 6 cm, we can use the formula for the volume of a sphere, which is given by:
V = (4/3)πr^3
Where V is the volume and r is the radius of the sphere.
Let's calculate the volume of the sphere with a radius of 4 cm:
V1 = (4/3)π(4^3)
= (4/3)π(64)
= (4/3)(3.14)(64)
= 268.19 cm^3
Now, let's calculate the volume of the sphere with a radius of 6 cm:
V2 = (4/3)π(6^3)
= (4/3)π(216)
= (4/3)(3.14)(216)
= 904.32 cm^3
The ratio of the volume of the sphere with a radius of 4 cm to the volume of the sphere with a radius of 6 cm can be calculated as:
V1/V2 = 268.19/904.32
≈ 0.2964
This ratio can be simplified by multiplying both the numerator and denominator by a suitable number to obtain whole numbers. In this case, multiplying by 100 will give us:
V1/V2 = (268.19*100)/(904.32*100)
≈ 29.64/100
≈ 29/100
Therefore, the ratio of the volume of a sphere of radius 4 cm to that of a sphere of radius 6 cm is approximately 29:100.
However, none of the given options match this ratio. Therefore, it seems that there may be an error in the options provided.
V = (4/3)πr^3
Where V is the volume and r is the radius of the sphere.
Let's calculate the volume of the sphere with a radius of 4 cm:
V1 = (4/3)π(4^3)
= (4/3)π(64)
= (4/3)(3.14)(64)
= 268.19 cm^3
Now, let's calculate the volume of the sphere with a radius of 6 cm:
V2 = (4/3)π(6^3)
= (4/3)π(216)
= (4/3)(3.14)(216)
= 904.32 cm^3
The ratio of the volume of the sphere with a radius of 4 cm to the volume of the sphere with a radius of 6 cm can be calculated as:
V1/V2 = 268.19/904.32
≈ 0.2964
This ratio can be simplified by multiplying both the numerator and denominator by a suitable number to obtain whole numbers. In this case, multiplying by 100 will give us:
V1/V2 = (268.19*100)/(904.32*100)
≈ 29.64/100
≈ 29/100
Therefore, the ratio of the volume of a sphere of radius 4 cm to that of a sphere of radius 6 cm is approximately 29:100.
However, none of the given options match this ratio. Therefore, it seems that there may be an error in the options provided.
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Find the ratio of the volume of a sphere of radius 4cm, to that of a sphere of radius 6 cm ?a)16:36b)27:8c)8:27d)36:16Correct answer is option 'C'. Can you explain this answer?
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