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The ratio of volumes of sphere X to that of sphere Y is 64 : 27. What
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19 Jun 2023, 05:42
19 Jun 2023, 05:42
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The ratio of volumes of sphere X to that of sphere Y is 64 : 27. What is the ratio of surface area of sphere X to that of sphere Y ?
A. 1 : 3
B. 9 : 16
C. 3 : 4
D. 4 : 3
E. 16 : 9
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A. 1 : 3
B. 9 : 16
C. 3 : 4
D. 4 : 3
E. 16 : 9
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE GEOMETRY
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Re: The ratio of volumes of sphere X to that of sphere Y is 64 : 27. What
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05 Jul 2023, 11:41
05 Jul 2023, 11:41
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Expert Reply
The ratio of volumes between two spheres is equal to the cube of the ratio of their radii. Let's assume that sphere X has a radius of r and sphere Y has a radius of s.
Given that the ratio of volumes of sphere X to sphere Y is 64:27, we can write the equation:
(Volume of X) / (Volume of Y) = (r³) / (s³) = 64/27
To find the ratio of surface areas, we need to determine the ratio of the radii. Taking the cube root of both sides of the equation, we get:
(r / s) = (4/3)
Now, let's calculate the ratio of surface areas. The surface area of a sphere is given by the formula:
Surface Area = 4πr²
The ratio of the surface areas of sphere X (SAx) to sphere Y (SAy) can be expressed as:
(SAx / SAy) = (4πr² / 4πs²) = (r² / s²)
Substituting the value of (r / s) from the previous equation, we have:
(SAx / SAy) = ((4/3)²) = (16/9)
Therefore, the ratio of the surface area of sphere X to the surface area of sphere Y is 16:9.
Answer: E
Given that the ratio of volumes of sphere X to sphere Y is 64:27, we can write the equation:
(Volume of X) / (Volume of Y) = (r³) / (s³) = 64/27
To find the ratio of surface areas, we need to determine the ratio of the radii. Taking the cube root of both sides of the equation, we get:
(r / s) = (4/3)
Now, let's calculate the ratio of surface areas. The surface area of a sphere is given by the formula:
Surface Area = 4πr²
The ratio of the surface areas of sphere X (SAx) to sphere Y (SAy) can be expressed as:
(SAx / SAy) = (4πr² / 4πs²) = (r² / s²)
Substituting the value of (r / s) from the previous equation, we have:
(SAx / SAy) = ((4/3)²) = (16/9)
Therefore, the ratio of the surface area of sphere X to the surface area of sphere Y is 16:9.
Answer: E
gmatclubot
Re: The ratio of volumes of sphere X to that of sphere Y is 64 : 27. What [#permalink]
05 Jul 2023, 11:41
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