Problem Solving

The volume of a large cube is 125 cubic inches. A new
shape is formed by removing a smaller cube from one
corner of the large cube. The surface area of this new
shape in square inches is

(a) 120
(b) 150
(c) 180
(d) 225
(e) 250

The answer is B.

The surface will not changed when you remove the smaller cube from the corner of the large cube.

Volume of cube = (side)^3
125 = (side)^3

Therefore side of the cube is 5 inches. Based on this the surface area of the large cube is
Surface Area = 6 x (side x side)
Surface Area = 6 x 5 x 5
Surface Area = 150 square inches.

Hence answer is B.

Hope this helps.

dtweah wrote:The volume of a large cube is 125 cubic inches. A new
shape is formed by removing a smaller cube from one
corner of the large cube. The surface area of this new
shape in square inches is

(a) 120
(b) 150
(c) 180
(d) 225
(e) 250

The fact that we're not given any length for the side of the smaller cube immediately made me guess that the surface of the new shape will be equal to that of the original cube, since there's nothing else we can calculate. Since the volume of the cube is 5^3 = 125, the side of the large cube is 5. A cube has 6 sides, each 5^2 = 25 in surface, with a total surface of 6*25 = 150.

I then imagined the whole thing and in my head at least I should be right .

ankitns wrote:The answer is B.

The surface will not changed when you remove the smaller cube from the corner of the large cube.

Volume of cube = (side)^3
125 = (side)^3

Therefore side of the cube is 5 inches. Based on this the surface area of the large cube is
Surface Area = 6 x (side x side)
Surface Area = 6 x 5 x 5
Surface Area = 150 square inches.

Hence answer is B.

Hope this helps.

dtweah wrote:The volume of a large cube is 125 cubic inches. A new
shape is formed by removing a smaller cube from one
corner of the large cube. The surface area of this new
shape in square inches is

(a) 120
(b) 150
(c) 180
(d) 225
(e) 250

not understanding. why won't surface area not change? you are removing cube, which diminishes surface for measurement...please break down.

thx

shahdevine wrote:

ankitns wrote:The answer is B.

The surface will not changed when you remove the smaller cube from the corner of the large cube.

Volume of cube = (side)^3
125 = (side)^3

Therefore side of the cube is 5 inches. Based on this the surface area of the large cube is
Surface Area = 6 x (side x side)
Surface Area = 6 x 5 x 5
Surface Area = 150 square inches.

Hence answer is B.

Hope this helps.

dtweah wrote:The volume of a large cube is 125 cubic inches. A new
shape is formed by removing a smaller cube from one
corner of the large cube. The surface area of this new
shape in square inches is

(a) 120
(b) 150
(c) 180
(d) 225
(e) 250

not understanding. why won't surface area not change? you are removing cube, which diminishes surface for measurement...please break down.

thx

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Try to visualize this: How many faces of the cube that is removed were contributing to the surface area? You would notice that its 3 sides. Now once the cube is removed how many faces are contributing to the surface area? Its the other 3 sides (that were inside the cube).
So the surface area does not really change!

not understanding. why won't surface area not change? you are removing cube, which diminishes surface for measurement...please break down.

thx

This is where your visualization skills come into play. When you take that cube out, you're still left with that cubical space on the corner of that larger cube. That cubical space still contains all the dimensions of the cube that was taken out, because think about it, the only area on the smaller cube that was taken into consideration was the area of the top face, the right side face, and the vertical downward face. The cubical space has all of these faces of the cube, but on opposite ends.