Question

Basic math plz help

volume of a cylinder with the given height and radius or diameter problems.

Answer 1

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Answer 2

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.

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
`(4)/(3)` with π and the cube of the radius (r³).

The sphere's volume ,
`V =`
`(4)/(3) \pi r^(3)`.

Step 4:

1. r = 5 cm,
`V =`
`(4)/(3) \pi r^(3)`,
`V = (4)/(3) (3.14) (5^(3)) = 523.333` cubic cm.

2. d = 24 inches, r = 12 inches,
`V =`
`(4)/(3) \pi r^(3)`,
`V = (4)/(3) (3.14) (12^(3)) = 7,234.56` cubic inches.

3. r = 1 foot,
`V =`
`(4)/(3) \pi r^(3)`,
`V = (4)/(3) (3.14) (1^(3)) = 4.18666` cubic feet.

4. d = 42 mm, r = 21 mm,
`V =`
`(4)/(3) \pi r^(3)`,
`V = (4)/(3) (3.14) (21^(3)) = 38,772.92` cubic mm.