Question

Each face of a small cube has a surface area of 0. 25 square meters. A larger cube has edges that are six times as long as the edges of the small cube. What is the volume of the larger cube?.

Answer 1

Surface area of small cube is square of its side. The volume of the larger cube is 27 meter cube.

What is volume of the cube?

The volume of the cube is the total space occupied by it in the 3 dimensional space.

The volume of the cube is given as,

$V=a^3$

Here, $a$ is the side of the cube.

Given information-

Each face of a small cube has a surface area of 0. 25 square meters.

A larger cube has edges that are six times as long as the edges of the small cube.

The surface area of a smaller cube is given as,

$A_s=a^2$

Here, $a$ is the side of the cube. As surface area of small cube is 0.25 square meters. Thus,

$0.25=a^2\\a=\sqrt{0.25}\\a=0.5$

As, the larger cube has edges that are six times as long as the edges of the small cube. Thus the side of the larger cube is,

$a_l=6\times0.5\\a_l=3\rm meter$

Thus the volume of the larger cube is,

$V=3^3\\V=27\rm m^3$

Thus the volume of the larger cube is 27 meter cube.

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