GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
The ratio of volumes of sphere X to that of sphere Y is 64 : 27. What
[#permalink]
19 Jun 2023, 05:42
19 Jun 2023, 05:42
Expert Reply
1
Bookmarks
00:00
Question Stats:
83% (01:17) correct
16% (00:47) wrong based on 6 sessions
Hide Show timer Statistics
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
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
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
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
Re: The ratio of volumes of sphere X to that of sphere Y is 64 : 27. What
[#permalink]
05 Jul 2023, 11:41
05 Jul 2023, 11:41
1
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
Moderators:
