Answer:
[tex] V_{total} = 26460 \pi~cm^3 [/tex]
[tex] V_{total} = 83127~cm^3 [/tex]
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
[tex] V_{total} = V_{upper~cone} + V_cylinder} + V_{lower~cone} [/tex]
[tex] V_{total} = \dfrac{1}{3} \pi r^2 h_1 + \pi r^2 h_2 + \dfrac{1}{3} \pi r^2 h_3 [/tex]
[tex] 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) [/tex]
[tex] 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) [/tex]
[tex] V_{total} = (147~cm^2)(35~cm)(\pi) + (441~cm^2)(35~cm)(\pi) + (147~cm^2)(40~cm)(\pi) [/tex]
[tex] V_{total} = 5145\pi~cm^3 + 15435\pi ~cm^3 + 5880\pi~cm^3 [/tex]
[tex] V_{total} = 26460 \pi~cm^3 [/tex]
[tex] V_{total} = 83127~cm^3 [/tex]
