Question

PLEASE HELP ME!! IM CURRENTLY DOING A DIAGNOSTIC AND HAVE ONLY 15 MINS LEFT !!!!! A toilet paper roll has a diameter of 8x and a height of 6x. The hole in the middle has a diameter of 2x. What is the simplified expression for the volume? NOTE THE FORMULA TO CALCULATE THE VOLUME OF A CYLINDER IS Volume= Pi * R ^2 * H Note: Use Pi for the answer. (EXAMPLE: 5pix^2)

Answer 1

Answer:

284/3 πx³

Step-by-step explanation:

Volume of a cylinder is expressed as shown:

V = πr²h

r is the radius of the cylinder

r = diameter/2

r = 8x/2

r = 4x

Height of the cylinder = 6x

Volume of the roll with out the hole

V = π(4x)²(6x)

V = 16x²π(6x)

V = 96πx³

The hole in the middle will be a solid sphere with diameter 2x (radius will be x)

Volume of the hole = 4/3πr³

Volume if the hole = 4/3πx³

Volume of the toilet paper roll = volume of the roll without a hole - volume of the hole

= 96πx³ - 4/3πx³

= (96-4/3)πx³

= 284/3 πx³