Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 8 meters cubed. Yolanda found the volume of the sphere.

Her work is shown below.


V = four-thirds (8) cubed.

V = four-thirds (512).

V = StartFraction 2,048 Over 3 EndFraction meters cubed.


What is Yolanda’s error?

A) Yolanda should have found the volume by multiplying 8 by Two-thirds.

B) Yolanda should have found the volume by multiplying 8 by Four-thirds.

C) Yolanda should have found the volume with the formula V = two-thirds pi (8) cubed.

D) Yolanda should have found the volume with the formula V = two-thirds (8) cubed.

Answer 1

B

Explanation:

Answer 2

Yolanda should have found the volume by multiplying 8 by four-thirds

Explanation:

Here, we want to find Yolanda’s error.

we proceed as follows;

Mathematically, the volume of the cylinder can be calculated using the formula;

V = pi * r^2 * h

now since the radius of the cylinder and the height is equal, we can say that h = r

and thus, the volume can be written as

V = pi * r^2 * r = pi * r^3

Mathematically, the volume of a sphere can be calculated using the formula

V = 4/3 * pi * r^3

Now from the question we know that the value of pi * r^3 =8 which is the value for the volume of the cylinder.

Thus the volume of the sphere would be 4/3 * 8

so the correct answer here is B