The volumes of the given cylinders ;
1. 125.6 cubic inches, 2. 62,800 cubic cm, 3. 2,009.6 cubic mm, and 4. 2,289.26 cubic feet.
The volumes of the given spheres;
1. 523.33 cubic cm, 2. 7,234.56 cubic inches, 3. 4.1866 cubic feet, and 4. 38,772.92 cubic mm.
Step-by-step explanation:
Step 1:
The volume of any cylinder is given by π times the product of the square of the radius (r²) and the height (h).
The volume of any cylinder, [tex]V =\pi r^{2} h[/tex].
Step 2:
1. d = 4 inches, r = 2 inches, h = 10 inches, [tex]V =\pi r^{2} h[/tex] [tex]= 3.14 (2^{2} )(10)[/tex] [tex]= 125.6[/tex] cubic inches.
2. r = 20 cm, h = 50 cm, [tex]V =\pi r^{2} h[/tex] [tex]= 3.14 (20^{2} )(50)[/tex] [tex]= 62,800[/tex] cubic cm.
3. d = 16 mm, r = 8 mm, h = 10 inches, [tex]V =\pi r^{2} h[/tex] [tex]= 3.14 (8^{2} )(10)[/tex] [tex]= 2,009.6[/tex] cubic mm.
4. r = 9 feet, h = 9 feet, [tex]V =\pi r^{2} h[/tex] [tex]= 3.14 (9^{2} )(9)[/tex] [tex]= 2,289.06[/tex] cubic feet.
Step 3:
The sphere's volume is given by multiplying [tex]\frac{4}{3}[/tex] with π and the cube of the radius (r³).
The sphere's volume , [tex]V =[/tex] [tex]\frac{4}{3} \pi r^{3}[/tex].
Step 4:
1. r = 5 cm, [tex]V =[/tex] [tex]\frac{4}{3} \pi r^{3}[/tex], [tex]V = \frac{4}{3} (3.14) (5^{3}) = 523.333[/tex] cubic cm.
2. d = 24 inches, r = 12 inches, [tex]V =[/tex] [tex]\frac{4}{3} \pi r^{3}[/tex], [tex]V = \frac{4}{3} (3.14) (12^{3}) = 7,234.56[/tex] cubic inches.
3. r = 1 foot, [tex]V =[/tex] [tex]\frac{4}{3} \pi r^{3}[/tex], [tex]V = \frac{4}{3} (3.14) (1^{3}) = 4.18666[/tex] cubic feet.
4. d = 42 mm, r = 21 mm, [tex]V =[/tex] [tex]\frac{4}{3} \pi r^{3}[/tex], [tex]V = \frac{4}{3} (3.14) (21^{3}) = 38,772.92[/tex] cubic mm.
