Find the volume I really need your help

Question

asked Sep 15, 2022 227k views

1 Answer

Brandon McConnell · Answer 1 · 2022-09-20T04:06:47+0000

Answer:

$V_(total) = 26460 \pi~cm^3$

V_(total) = 83127~cm^3

Explanation:

The solid is made up of 2 cones and a cylinder.

Upper cone:

radius = 21 cm

height = h_1 = 70 cm - 35 cm = 35 cm

Cylinder:

radius = 21 cm

height = h_2 = 35 cm

Lower cone:

radius = 21 cm

height = h_3 = 40 cm

V_(total) = V_(upper~cone) + V_cylinder} + V_(lower~cone)

$V_(total) = (1)/(3) \pi r^2 h_1 + \pi r^2 h_2 + (1)/(3) \pi r^2 h_3$

$V_(total) = (1)/(3)(\pi)(21~cm)^2(35~cm) + (\pi)(21~cm)^2(35~cm) + (1)/(3)(\pi)(21~cm)^2(40~cm)$

$V_(total) = (1)/(3)(\pi)(441~cm^2)(35~cm) + (\pi)(441~cm^2)(35~cm) + (1)/(3)(\pi)(441~cm^2)(40~cm)$

$V_(total) = (147~cm^2)(35~cm)(\pi) + (441~cm^2)(35~cm)(\pi) + (147~cm^2)(40~cm)(\pi)$

$V_(total) = 5145\pi~cm^3 + 15435\pi ~cm^3 + 5880\pi~cm^3$

$V_(total) = 26460 \pi~cm^3$

V_(total) = 83127~cm^3