Question

Basic math plz help volume of a cylinder with the given height and radius or diameter problems.

Answer 1

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, $V =\pi r^{2} h$.

Step 2:

1. d = 4 inches, r = 2 inches, h = 10 inches, $V =\pi r^{2} h$ $= 3.14 (2^{2} )(10)$ $= 125.6$ cubic inches.

2. r = 20 cm, h = 50 cm, $V =\pi r^{2} h$ $= 3.14 (20^{2} )(50)$ $= 62,800$ cubic cm.

3. d = 16 mm, r = 8 mm, h = 10 inches, $V =\pi r^{2} h$ $= 3.14 (8^{2} )(10)$ $= 2,009.6$ cubic mm.

4. r = 9 feet, h = 9 feet, $V =\pi r^{2} h$ $= 3.14 (9^{2} )(9)$ $= 2,289.06$ cubic feet.

Step 3:

The sphere's volume is given by multiplying $\frac{4}{3}$ with π and the cube of the radius (r³).

The sphere's volume , $V =$ $\frac{4}{3} \pi r^{3}$.

Step 4:

1. r = 5 cm, $V =$ $\frac{4}{3} \pi r^{3}$, $V = \frac{4}{3} (3.14) (5^{3}) = 523.333$ cubic cm.

2. d = 24 inches, r = 12 inches, $V =$ $\frac{4}{3} \pi r^{3}$, $V = \frac{4}{3} (3.14) (12^{3}) = 7,234.56$  cubic inches.

3. r = 1 foot, $V =$ $\frac{4}{3} \pi r^{3}$, $V = \frac{4}{3} (3.14) (1^{3}) = 4.18666$ cubic feet.

4. d = 42 mm, r = 21 mm, $V =$ $\frac{4}{3} \pi r^{3}$, $V = \frac{4}{3} (3.14) (21^{3}) = 38,772.92$  cubic mm.