A Plastic Travel Mug Is Made in Two Parts, the Cup

Short Answer

A plastic travel mug is made in two parts, the cup and the base.The cup part has outside shape $y=\sqrt{x}$ and inside shape $y=\sqrt[4]{x}$ cut off at x = 4 as shown in the following figure. If the cup is 14 cm tall, and the base is 10 cm in diameter and 1 cm thick, find the volume of plastic needed to make the mug.Round to 2 decimal places.