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.
In the cube above, the length of line segment AB is
[#permalink]
30 Jul 2017, 11:06
30 Jul 2017, 11:06
1
Expert Reply
1
Bookmarks
00:00
Question Stats:
81% (01:04) correct
18% (01:20) wrong based on 103 sessions
Hide Show timer Statistics
Attachment:
#GREpracticequestion In the cube above, the length of line segment AB is 8.jpg [ 24.45 KiB | Viewed 6755 times ]
In the cube above, the length of line segment AB is 8. The surface area of the cube equals what?
enter your value
Show: :: OA
192
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In the cube above, the length of line segment AB is
[#permalink]
30 Jul 2017, 17:59
30 Jul 2017, 17:59
3
Carcass wrote:
Attachment:
shot3.jpg
In the cube above, the length of line segment AB is 8. The surface area of the cube equals what?
enter your value
Show: :: OA
192
Each face of the cube is a SQUARE, and there are 6 faces on a cube.
Imagine a square with sides of length x and a diagonal with length 8
The diagonal divides the square into to right triangles.
Focus on one of the right triangles.
The two legs have length x, and the hypotenuse (aka diagonal) has length 8
Applying the Pythagorean Theorem, we can write: x² + x² = 8²
Simplify: 2x² = 64
Divide each side by 2 to get: x² = 32
IMPORTANT: we need not go any further and solve for x.
Why not you ask?
Well, the question asks us to find the surface area of the cube.
Since each face of the cube is a SQUARE, we need to find the area of each of the 6 identical squares.
Area of a square = (base)(height) = (x)(x) = x²
Hey, we already know that x² = 32
So, the area of each of the cube's 6 squares is 32
So, the total surface area = (6)(32) = 192
Cheers,
Brent
Re: In the cube above, the length of line segment AB is
[#permalink]
11 Sep 2019, 07:12
11 Sep 2019, 07:12
1
One could also use an alternate formula for the area of a square, rhombus or kite. It's not useful very often, but in cases like this, it could save a little time if you know it. Here it is:
Area of square, rhombus or kite = \(\frac{diagonalOne • diagonalTwo}{2}\)
We were given the diagonal for the bottom square was 8. A property of squares is both diagonals are identical. So, we have diagonal 1 of the square = 8, and diagonal 2 of the square = 8. We can plug that into our formula.
Area of square, rhombus or kite = \(\frac{8 • 8}{2} = 64/2 = 32\)
So, we have the area of one face of the cube. It is 32. So we can express that as a ratio of 32 units/1 face. It is known that cubes have six faces. If we multiply that by the ratio, we'll have the total number of square units for the surface area of the cube.
6 faces •\(\frac{32}{1Face}\) = 192
Area of square, rhombus or kite = \(\frac{diagonalOne • diagonalTwo}{2}\)
We were given the diagonal for the bottom square was 8. A property of squares is both diagonals are identical. So, we have diagonal 1 of the square = 8, and diagonal 2 of the square = 8. We can plug that into our formula.
Area of square, rhombus or kite = \(\frac{8 • 8}{2} = 64/2 = 32\)
So, we have the area of one face of the cube. It is 32. So we can express that as a ratio of 32 units/1 face. It is known that cubes have six faces. If we multiply that by the ratio, we'll have the total number of square units for the surface area of the cube.
6 faces •\(\frac{32}{1Face}\) = 192
