Question

What was Mia's first error? She confused the height and the diameter. She forgot to include pi as a factor in the volume expression. She applied the exponent before multiplying 17.5 and 47. She squared 17.5 instead of 35.

Answer 1

She forgot to include pi as a factor in the volume expression.

Explanation:

The exact question is as follows :

Given - Mia is calculating the volume of the cylinder below using the following work.

A cylinder with height of 47 meters and diameter of 35 meters.

To find - What was Mia’s first error?

1. She confused the height and the diameter.
2. She forgot to include pi as a factor in the volume expression.
3. She applied the exponent before multiplying 17.5 and 47.
4. She squared 17.5 instead of 35.

Solution -

Given that,

Diameter of cylinder = 35 centimeter

Height of cylinder = 47 centimeter

Now,

We know that,

Volume of cylinder, V =
`\pi`r²h

Also,

We know, Diameter = 2×Radius

⇒Radius = Diameter ÷ 2

= 35 ÷ 2

= 17.5

⇒Radius = 17.5

SO,

The volume becomes, V =
`\pi`(17.5)²(47)

=
`\pi`(306.25)(47)

= 14393.75
`\pi`

So,

The volume of the cylinder becomes 14393.75
`\pi` m³

But

Mia calculated the Volume is 14393.75

By comparing with the actual Volume, we get

The Mia's first error is - She forgot to include pi as a factor in the volume expression.