How to make a paper cup that can hold water

Asked by admin @ 30/10/2021 in Mathematics viewed by 309 People

A 6 oz paper cup is shaped like a cone with a diameter of 4 inches. How many ounces of water will a plastic cylindrical cup with a diameter of 4 inches hold if it is the same height as the paper cup?

Answered by admin @ 30/10/2021

Answer:

The plastic cylindrical cup will hold 17.96 ounces of water.

Step-by-step explanation:

Given:

A 6 oz paper cup is shaped like a cone with a diameter of 4 inches.

Now, to find ounces of water will a plastic cylindrical cup with a diameter of 4 inches hold if it is the same height as the paper cup.

Volume of cone = 6 oz.

Diameter = 4 inches.

So, radius (r) = $\frac{Diameter}{2} =\frac{4}{2} =2\ inches.$

Taking the value $\pi$ = 3.14.

Now, to get the height (h) we put formula:

$Volume=\pi r^2\frac{h}{3}$

$Volume=3.14\times 2^2\times \frac{h}{3}$

$6=3.14\times 4\times \frac{h}{3}$

Multiplying both sides by 3 we get:

$18=12.56h$

Dividing both sides by 12.56 we get:

$1.43=h$

$h=1.43\ inches.$

Now, to get the volume of cylindrical cup.

As, given it is the same height as the paper cup.

Height (h) = 1.43 inches.

Diameter = 4 inches.

Radius (r) = $\frac{Diameter}{2} =\frac{4}{2} =2\ inches.$

So, we put formula to get the ounces of water a plastic cylindrical cup will hold:

$Volume =\pi r^2h$

$Volume=3.14\times 2^2\times 1.43$

$Volume=3.14\times 4\times 1.43$

$Volume=17.96\ oz.$

Therefore, the plastic cylindrical cup will hold 17.96 ounces of water.

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