Find the height for each solid given the volume as follows: 4. A cone with a volume of 238cm 3 5. A cylinder with volume = 424 in 3 Radius = 4in Radius = 8in 5. Find the radius of a sphere if the volume is 362 in.

The correct question is;

Find the height for each solid given the volume as follows:

4. A cone with a volume of 238cm³ with radius = 4cm

5. A cylinder with volume = 424 in³ Radius = 4in and Radius = 8in

6. Find the radius of a sphere if the volume is 362 in.

Answer:

1. h ≈ 14.2 cm

2. For radius of 8 inches, height = 2.11 in

For radius of 4 inches, height = 8.44 in

3. r = 9.48 in

Step-by-step explanation:

1) a cone with a volume of 238cm

Formula for volume of a cone is;

V = ⅓πr²h

Radius = 4cm

So, 238 = ⅓π * 4² * h

h = (238 * 3) / (16 * π)

h ≈ 14.2 cm

2) Volume of cylinder is given as;

V = πr²h

Radius, r = 8 in and volume, V = 424 in³

Thus, h = V/πr²

h = 424 / (π * 8²)

h = 2.11 in

For a radius of 4 in, h = 424 / (π * 4²)

h = 8.44 in

3) volume of sphere is;

V = (4/3) πr³

r³ = 3V/4π

r = ∛ (3V/4π)

We are given that volume = 362 in³

So, r = ∛ (3*362/4π)

r = 9.48 in