If the surface area of a cylinder with a radius of 4 inches and a

GMATinsight, IMHO, question says surface area and not total surface area of the cylinder. To me, surface area of a cyliner = \(2*\pi*r*h\) while total surface area = surface area + \(2*\pi*r^2\)

It's a battle of "Opinions" so Let's wait for the Answer

Solution -

This will be absolutely total surface area of Cylinder comparing with surface area of Cube.

Surface Area of A Cylinder = 2*π*r(r+h)=2*π*4(4+10)=112*π=112*(22/7)=352

Surface Area of Cube = 6*Side^2=352 ---> Side^2=58.6 ---> Side =7.6 ≈ 8 ANS E

800score Official Solution:

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).

Bunuel, can you clarify whether this question is ambiguous in the use of the term "surface area". To me , surface area = curved surface area of the cylinder = \(2\pi rh\) while the solution calculates TOTAL SURFACE AREA .

These 2 quantities are different. So is it implied that GMAT will mean total surface area when calling out "surface area" in the question?

There are two examples in OG and Quant Review about the surface area of a cylinder. In both it's TOTAL surface area. Here is what OG says:

The surface area of a right circular cylinder with a base of radius r and height h is equal to \(2(\pi r^2) + 2\pi rh\) (the sum of the areas of the two bases plus the area of the curved surface).

Hope it's clear.

Thanks Bunuel. Yes it does help.

2 * (pi) * (r) * [h+r] = 6 * (a)^2
112 (pi) = 6(a^2)
a^2 = (112*22)/(7*6) = 58.66
Hence, a ~ 8. Ans (E).

You were correct in your definition of surface area for GMAT questions.

Length of the cube side= a
Surface area the cube= 6 a2 = surface area of cylinder = 2 π r h + 2 π r2
Or, 6a2 = 2 π x 4 x 10 + 2 π 42 = 112 π
Or, a2 ≈ 19 π ≈ 58
Or, a ≈ 8

Cylinder = circumference*height + 2 end caps
Cube = 6 * sides
Cylinder = (2*pi*4)* 10 + 16*pi + 16*pi =112*pi
cube = 6*x^2
6*x^2=112*pi
assume pi=3
2*x^2=112
x^2=56
x=8

Pretty rough math but it get's you there

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.