Question

Find the volume I really need your help

Answer 1

Answer:

$V_{total} = 26460 \pi~cm^3$

$V_{total} = 83127~cm^3$

Step-by-step 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

$V_{total} = V_{upper~cone} + V_cylinder} + V_{lower~cone}$

$V_{total} = \dfrac{1}{3} \pi r^2 h_1 + \pi r^2 h_2 + \dfrac{1}{3} \pi r^2 h_3$

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

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

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

$V_{total} = 5145\pi~cm^3 + 15435\pi ~cm^3 + 5880\pi~cm^3$

$V_{total} = 26460 \pi~cm^3$

$V_{total} = 83127~cm^3$