A sphere and a cylinder have the same radius and height. The volume of the cylinder is 54 meters cubed. Amie found the volume of

Question

2 years ago

10

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 54 meters cubed. Amie found the volume of

the sphere.
A sphere with height h and radius r. A cylinder with height h and radius r.

Her work is shown below.

V = two-thirds + 54. V = two-thirds + StartFraction 162 Over 3 EndFraction. V = StartFraction 164 Over 3 EndFraction meter cubed.

What is Amie’s error?
Amie should have multiplied 54 by Two-thirds.
Amie should have multiplied 54 by Four-thirds pi.
Amie should have multiplied 54 by Four-thirds.
Amie should have multiplied 54 by Two-thirds pi.

Mathematics

1 answer:

MatroZZZ [7] · Answer 1 · 2023-10-07T11:47:59+03:00

The error in Amie's evaluation as described in the task content is; Amie should have multiplied 54 by Two-thirds.

<h3>What is Amie's error in the evaluation?</h3>

Since it follows that the she needs the volume of the sphere in which case the radius of the sphere is half the height.

Hence we have;

V(sphere) = (4/3) πr² × h/2

V = (2/3) × πr²h

Where πr²h = Volume of the cylinder = 54cm

Hence, Amie should have multiplied 54 by Two-thirds.