Question

Kiran decides to estimate the volume of a coffee cup by modeling it as a right cylinder. Kiran measures its circumference as 16.4 cm and its volume as 165 cubic centimeters. Find the height of the cup in centimeters. Round your answer to the nearest tenth if necessary.

Answer 1

h = 7.8 cm

Explanation:

Mensuration:

We can find the radius of the cup from the circumference of the cup.

`\sf ~~~~~~~~~~2\pi r = 16.4 \ cm\\\\2*3.14*r = 16.4\\\\~~~~~~~~~~~~~~r = (16.4)/(2*3.14)\\\\\\\boxed{\bf r = 2.6 \ cm}`

Now, we can find the height of the cup.

Volume of cylindrical cup = πr²h

πr²h = 165 cm³

`\sf 3.14 * 2.6 *2.6 * h = 165\\\\`

`\sf h = (165)/(3.14*2.6*2.6)\\\\\boxed{\bf h = 7.8 \ cm}`