Dimensions of a paper cup. The volume of a paper cup, shaped like a circular cone is 30pie cubic centimeters. The radius of the top of the cup is 3 centimeters. What is the height of the cup?
v = (1/3)(π)(r^2)h
30pi cm^3=(1/3)(π)(3^2)h
find h.
v = (1/3)(ð)(r^2)h
3v = ð (r^2)h
3v/ð = (r^2)h
3v/ð(r^2)= h
To find the height of the paper cup, we can use the formula for the volume of a cone. The formula is given by V = (1/3) * π * r^2 * h, where V is the volume, π is pi (approximately 3.14159), r is the radius of the top of the cone, and h is the height of the cone.
Given that the volume of the cup is 30π cubic centimeters and the radius of the top is 3 centimeters, we can substitute these values into the formula:
30π = (1/3) * π * 3^2 * h
Simplifying the equation:
30π = (1/3) * π * 9 * h
Cancelling π on both sides of the equation:
30 = (1/3) * 9 * h
Multiplying both sides by 3:
90 = 9 * h
Finally, dividing both sides by 9:
h = 10
Therefore, the height of the paper cup is 10 centimeters.