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 Post subject: GMAT 3D Geometry Posted: Wed Aug 04, 2010 4:31 am Joined: Sun May 30, 2010 3:15 am
Posts: 424
If the surface area of a cylinder with a radius of 4 inches and a height of 10 inches is equal to the surface area of a cube, which of the following is approximately equal to the length of one of the cube's edges?
A. 3
B. 4
C. 5
D. 6
E. 8

(E) The first step in answering this question, is to determine the surface area of the cylinder and then set it equal to the surface area of the cube.

The cylinder can be broken down into two circular caps and a rectangular body whose length is equal to the circumference of each circular cap, and whose height is given. GMAT students should be familiar with taking areas of circles and rectangles. Each circular cap will have a surface area of: 4² × π, or 16π. Since we have two such caps, the sum of their areas must be equal to 32π square inches.

Next, we want to determine the surface area of the cylindrical body. The latter is equal to the circumference of the circle multiplied by height, 8π × 10 = 80π square inches.

So, the cylindrical surface area is equal to the sum of the areas we found: 80π + 32π = 112π square inches.

The next task requires that we set the surface area equal to the surface area of a cube. For now, let us choose the edge length of the cube to be x. The surface area of the cube is equal to the product of the number of faces and the area of each face (recall that each face of a cube is a square): 6x².

We set the two quantities equal to each other: 6x² = 112π. We can now solve this equation by dividing both sides by 6 and taking the square root of both sides:
x = √(112π / 6).

Since the question asks us to approximate, we can let π equal 3. After the substitution we are left with √56, which is approximately equal to 8 or answer choice (E).
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The solution is incorrect as Surface area of cylinder is 2πr² + 2πrh where r is radius and h is height.

Your solution incorrectly calculates area of cylinderical body by not considering the height.

Top Post subject: Re: Math (test 1, question 14): geometry, surface area Posted: Wed Aug 04, 2010 5:22 am Joined: Sun May 30, 2010 2:23 am
Posts: 498
Note, that we do multiply by height when we calculate the area of cylindrical body.

Let us draw graphics for this question. Here we have a cylinder:

We brake it down in parts when calculate the area:

The area of caps is calculated as the area of circles:

Each cap: 4² × π = 16π
Both caps: 32π (square inches)

The area of the body is calculated as the area of the rectangle:

8π × 10 = 80π (square inches)

Then we add the areas. 80π + 32π = 112π (square inches)

When we calculate area of a cube we break it down in squares:

We can see that there are 6 identical squares:

The area of each one is x²
The area of all six is 6x²

At last, we set the areas equal:
6x² = 112π (square inches)

And find that approximation of x to an integer is 8 (inches).

 Attachments: square.gif [2.14 KiB] Not downloaded yet cube.gif [15.64 KiB] Not downloaded yet body.gif [2.91 KiB] Not downloaded yet cap1.gif [4.06 KiB] Not downloaded yet body_colored.gif [4.97 KiB] Not downloaded yet caps_colored.gif [4.6 KiB] Not downloaded yet cylinder1.gif [4.66 KiB] Not downloaded yet
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