Finding the Volume of a Cone

The video tutorial by Mr. J explains how to find the volume of a cone using the formula 1/3 times the area of the base times the height. The base of a cone is a circle, so the area is calculated using pi r squared. The tutorial provides two examples: one with a given radius and another with a given diameter. It also explains why the volume of a cone is one-third of a cylinder with the same base and height. The video concludes with a summary of the steps and encourages viewers to practice the calculations.

What is the formula for finding the volume of a cone?

• Volume = 2 * Pi * r * height

• Volume = base area * height

• Volume = 1/3 * base area * height

• Volume = Pi * r^2 * height

How do you calculate the area of a cone's circular base?

• Pi * radius

• 2 * Pi * radius

• Pi * diameter

• Pi * radius^2

What is the first step in calculating the volume of a cone?

• Multiply the height by Pi

• Square the height

• Divide the diameter by two to find the radius

• Calculate the area of the base

What is the volume of a cone with a radius of 5 inches and a height of 12 inches, in terms of Pi?

• 100 Pi cubic inches

• 60 Pi cubic inches

• 25 Pi cubic inches

• 300 Pi cubic inches

How do you simplify the expression 25 * 12 in the context of finding a cone's volume?

• By subtracting 12 from 25

• By dividing 25 by 12

• By adding 25 and 12

• By multiplying 25 and 12

What is the exact volume of a cone with a radius of 5 inches and a height of 12 inches?

• 150 Pi cubic inches

• 314.16 cubic inches

• 314 cubic inches

• 100 cubic inches

Why is the volume of a cone one-third the volume of a cylinder with the same base and height?

• Because a cone is half the size of a cylinder

• It's a mathematical coincidence

• The cone occupies one-third of the cylinder's space

• Due to the cone's pointed shape

How do you find the radius from the diameter?

• Multiply the diameter by 2

• Square the diameter

• Divide the diameter by 2

• Take the square root of the diameter

What is the volume of a cone with a diameter of 14 cm and height of 8 cm, in terms of Pi?

• 392/3 Pi cubic centimeters

• 100 Pi cubic centimeters

• 49 Pi cubic centimeters

• 392 Pi cubic centimeters

What is the exact volume of a cone with a diameter of 14 cm and height of 8 cm, rounded to the nearest hundredth?

• 123.20 cubic centimeters

• 410.50 cubic centimeters

• 392 cubic centimeters

• 130.67 cubic centimeters