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?
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
Thank You
To find the depth of the cup, we can use the volume formula for a right circular cone, which is:
V = (1/3)πr²h
Where V is the volume, r is the radius of the circular base, and h is the height or depth of the cone.
Given: V = 250 milliliters and r = 6 centimeters
Converting milliliters to cubic centimeters, we can rewrite the volume as:
V = 250 cm³
Now we can substitute the given values into the formula and solve for h:
250 = (1/3)π(6²)h
First, we simplify the expression:
250 = (1/3)π(36)h
Next, we can cancel out the common factor of 3:
3 * (250) = π(36)h
750 = π(36)h
To isolate h, divide both sides by π(36):
h = 750 / (π(36))
Finally, we can simplify the expression and calculate the depth of the cup:
h ≈ 750 / (3.14 * 36)
h ≈ 750 / 1130.24
h ≈ 0.663 cm
Therefore, the depth of the cup is approximately 0.663 centimeters.