Question

A cone is cut out of the center of a pyramid with a rectangular base. The rectangular base has side lengths of 15 and 10 units. The cone has a diameter of 9 and a height of 12. The pyramid and cone have the same height. What is the volume of the shaded portion of the composite figure? Express your answer in terms of π. 519π units3 681π units3 (600π – 81) units3 (600 – 81π) units3

Answer 1

Answer:

Volume of shaded portion = (600 - 36π) units³

Step-by-step explanation:

Volume of the shaded portion = Volume of pyramid - Volume of cone

Volume of pyramid = ⅓*l*w*h

Where,

l = length of base of pyramid = 15 units

w = width of base of pyramid = 10 units

h = height of pyramid = 12 units

Plug in the values to find the volume of the pyramid

Volume of pyramid = ⅓*15*10*12 = 5*10*12 = 600 units³

Volume of Cone = ⅓πr²h,

Where,

r = radius = ½ of diameter = ½ of 9 = 3 units

h = height = 12 units

Volume of Cone = ⅓*π*3²*12 = ⅓*π*9*12

= π*3*12 = 36π units³

Volume of shaded portion = (600 - 36π) units³