Answer:
a) 640.32 cm^3
b) 98.4 cm^3
Step-by-step explanation:
Part a)
Cylinder volume:
(3.14) × 2^2 × 12 = 150.72 cm^3
Triangular prism:
We need to find the height of the base so we use the Pythagorean theorem.
5^2 + x^2 = 14.1^2
25 + x^2 = 198.81
x^2 = 173.81
x = 13.184
After finding height, we can use the equation for a normal triangular prism:
[tex]\frac{1}{2}[/tex] × Base × Height × Length
[tex]\frac{1}{2}[/tex] × 13.184 × 10 × 12= 791.04cm^3
Total Volume: 791.04 - 150.72 = 640.32 cm^3
Part b)
Small Sphere Volume:
[tex]\frac{4}3[/tex] × 3.14 × 1^3 = [tex]\frac{314}{75}[/tex]cm^3
Half Sphere Volume :
0.5([tex]\frac{4}3[/tex]× 3.14 × 3^3) = 56.52cm^3
Cone Height:
5^2 = 3^2 + h^2
25 = 9 + h^2
16 = h^2
h = 4
Cone Volume:
(3.14) × 3^2 × [tex]\frac{4}{3}[/tex] = 37.68 cm^3
Total Volume = 98.4 after rounding
