Question

Which of the following statements is correct? * A. If the edge of a cube is multiplied by 4, the volume of the cube is multiplied by a factor of 64. B. If the edge of a cube is multiplied by 5, the surface area of the cube is multiplied by 30. C. If the radius of a sphere is doubled, the volume of the sphere is multiplied by a factor of 4. D. If the edge of a cube is multiplied by 4, the volume of the cube is multiplied by a factor of 16.

Answer 1

option A only is correct

Explanation:

Here we want to evaluate the validity of some claims;

A. Mathematically; the volume of a cube is L^3

Now let’s multiply the length by 4 and the new length becomes 4L

The new volume would thus be (4L)^3 = 64 L^3

This is correct

B. Mathematically the area of a cube is;

6L^2. Now let’s multiply the length by 5 and the new length becomes 5L

The new volume is thus ;

6 * 5L * 5L = 150L^2 = 25(6L^2)

So this is wrong

C. Mathematically; area of a sphere is;

4/3 * pi * r^3

double the radius and the new radius becomes 2r

The volume is thus;

4/3 * pi * (2r)^3

= 4/3 * pi * 8r^3 = 32/3 * pi * r^3

We can see that the later answer is 8 times the former which makes the option wrong too

D. Volume of cube is L^3

Now let’s find the new volume at a length of 4L

(4L)^3 = 64L^3

we can see that the new is 64 times the old which makes this wrong