A perfectly spherical satellite with a radius of 4 feet is being packed for shipment to its launch site. If the inside dimensions of the rectangular crates available for shipment, when measured in feet, are consecutive even integers, then what is the volume of the smallest available crate that can be used?
(Note: the volume of a sphere is given by the equation v=(4/3)pie r^3 .)
(A) 48
(B) 192
(C) 480
(D) 960
(E) 1,680
OA D
Source: Princeton Review
A perfectly spherical satellite with a radius of 4 feet is
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Given: Radius of the spherical satellite = 4ft, so diameter = 8 ftBTGmoderatorDC wrote:A perfectly spherical satellite with a radius of 4 feet is being packed for shipment to its launch site. If the inside dimensions of the rectangular crates available for shipment, when measured in feet, are consecutive even integers, then what is the volume of the smallest available crate that can be used?
(Note: the volume of a sphere is given by the equation v=(4/3)pie r^3 .)
(A) 48
(B) 192
(C) 480
(D) 960
(E) 1,680
OA D
Source: Princeton Review
The minimum dimension of the rectangular box (crate) must be 8*8*8 in order for the spherical satellite to perfectly fit into the crate.
Since the dimensions of the crate are consecutive even integers, the minimum values of the dimensions of the crates must be 8, 8 + 2 = 10 and 10 + 2 = 12
=> Volume of the rectangular box (Crate) = 8*10*12 = 960 ft^3
The correct answer: D
Hope this helps!
-Jay
_________________
Manhattan Review GRE Prep
Locations: GMAT Classes Chicago | GRE Prep Course San Diego | GRE Prep Atlanta | TOEFL Prep Classes Houston | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Since the radius is 4 feet, the smallest side should be equal to the diameter. Hence the shortest side will be 8 feet and therefore the rest of the sides will be 10 and 12 feet.
Volume will be 8 x 10 x 12 = 960 ft^3. Regards!
Volume will be 8 x 10 x 12 = 960 ft^3. Regards!
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7249
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
The shortest dimension of the rectangular crate has to be at least the diameter of the spherical satellite; therefore, that dimension has to be at least 8. Since the dimensions of the crate are consecutive even integers, the smallest possible volume of the crate is:BTGmoderatorDC wrote:A perfectly spherical satellite with a radius of 4 feet is being packed for shipment to its launch site. If the inside dimensions of the rectangular crates available for shipment, when measured in feet, are consecutive even integers, then what is the volume of the smallest available crate that can be used?
(Note: the volume of a sphere is given by the equation v=(4/3)pie r^3 .)
(A) 48
(B) 192
(C) 480
(D) 960
(E) 1,680
8 x 10 x 12 = 960
Answer: D
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews