A soft-drink cup is in the shape of a right circular cone with capacity 250 milliliters. The radius of the circular base is 6 centimeters. How deep is the cup?

Answer 1

1 dm³ = 1 L

1 dm = 10 cm

1 L = 1 dm³ = 10³ cm³

1 L = 1000 cm³

1 L = 1000 mL

1000 cm³ = 1000 mL

1 cm³ = 1 mL

250 mL = 250 / 1000 L = 0.25 L = 0.25 ∙ 1000 cm³ = 250 cm³

The volume of a cone is given by:

V = π ∙ r² ∙ h / 3

250 = π ∙ 6² ∙ h / 3

250 = π ∙ 36 ∙ h / 3

Multiply both sides by 3

780 = 36 π ∙ h

Divide both sides by 36 π

780 / 36 π = h

780 / 36 ∙ 3.14 = h

780 / 113.04 = h

6.634819533‬ = h

h = 6.634819533 cm

Answer 2

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