Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is . Amie found the volume of the sphere. Her work is shown below. What is Amies error

Answer 1

Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.

In the question, we are given that a sphere and a cylinder have the same radius and height.

We assume the radius of the sphere to be r, and its height to be h.

Now, the height of a sphere is its diameter, which is twice the radius.

Thus, the height of the sphere, h = 2r

Given that the sphere and the cylinder have the same radius and height, the radius of the cylinder is r, and its height is 2r.

The volume of a sphere is given by the formula, V = (4/3)πr³, where V is its volume, and r is its radius.

Thus, the volume of the given sphere using the formula is (4/3)πr³.

The volume of a cylinder is given by the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.

Thus, the volume of the given cylinder using the formula is πr²(2r) = 2πr³.

Now, to compare the two volumes we take their ratios, as

Volume of the sphere/Volume of the cylinder

= {(4/3)πr³}/{2πr³}

= 2/3.

Thus, the volume of the sphere/the volume of the cylinder = 2/3,

or, the volume of the sphere = (2/3)*the volume of the cylinder.

Given the volume of the cylinder to be 54 m³, Amie should have multiplied 54 by 2/3 instead of adding the two.

Thus, Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.

Learn more about volumes at

brainly.com/question/12398192

#SPJ4

For the complete question, refer to the attachment.