How to find the volume of a cone - PSAT Math

The volume of a cone is given by the formula V = (πr2)/3. In order to determine how many seconds it will take for the tank to fill, we must divide the volume by the rate of flow of the water.

time in seconds = (πr2)/(3w)

In order to convert from seconds to minutes, we must divide the number of seconds by sixty. Dividing by sixty is the same is multiplying by 1/60.

(πr2)/(3w) * (1/60) = π(r2)(h)/(180w)

The basic form for the volume of a cone is:

V = (1/3)πr_2_h

For this simple problem, we merely need to plug in our values:

V = (1/3)π_132 * 6 = 169 * 2_π = 338_π_ in3

The general formula is given by V = 1/3Bh = 1/3pi $r^{2}$h, where = radius and = height.

The diameter is 6 cm, so the radius is 3 cm.

First we will calculate the volume of the cone

Next we will determine the time it will take to fill that volume

We will then convert that into minutes

The radius and the height of a cone are required in order to find its volume.

The radius is 50 centimeters, which can be converted to meters by dividing by 100:

meters

The slant height is 120 centimeters, which converts similarly to

meters

To find the height, we need to use the Pythagorean Theorem with the radius 0.5 as one leg and the slant height 1.2 as the hypotenuse of a right triangle, and the height as the other leg:

meters.

The volume formula can now be used:

cubic meters

The fomula for the volume of a cone is

Because our radius of the base is , we know that .

.

The volume of a cone is given by the formula V = (πr2)/3. In order to determine how many seconds it will take for the tank to fill, we must divide the volume by the rate of flow of the water.

time in seconds = (πr2)/(3w)

In order to convert from seconds to minutes, we must divide the number of seconds by sixty. Dividing by sixty is the same is multiplying by 1/60.

(πr2)/(3w) * (1/60) = π(r2)(h)/(180w)

The basic form for the volume of a cone is:

V = (1/3)πr_2_h

For this simple problem, we merely need to plug in our values:

V = (1/3)π_132 * 6 = 169 * 2_π = 338_π_ in3

There are two things to be careful with here. First, we must solve for the radius of the base. Secondly, note that the height is given in feet, not inches. Notice that all the answers are in cubic inches. Therefore, it will be easiest to convert all of our units to inches.

First, solve for the radius, recalling that C = 2_πr_, or, for our values 77_π_ = 2_πr_. Solving for r, we get r = 77/2 or r = 38.5.

The height, in inches, is 24.

The basic form for the volume of a cone is: V = (1 / 3)πr_2_h

For our values this would be:

V = (1/3)π * 38.52 * 24 = 8 * 1482.25_π_ = 11,858π in3

The general formula is given by V = 1/3Bh = 1/3pi $r^{2}$h, where = radius and = height.

The diameter is 6 cm, so the radius is 3 cm.

First we will calculate the volume of the cone

Next we will determine the time it will take to fill that volume

We will then convert that into minutes

The radius and the height of a cone are required in order to find its volume.

The radius is 50 centimeters, which can be converted to meters by dividing by 100:

meters

The slant height is 120 centimeters, which converts similarly to

meters

To find the height, we need to use the Pythagorean Theorem with the radius 0.5 as one leg and the slant height 1.2 as the hypotenuse of a right triangle, and the height as the other leg:

meters.

The volume formula can now be used:

cubic meters

The fomula for the volume of a cone is

Because our radius of the base is , we know that .

.

The volume of a cone is given by the formula V = (πr2)/3. In order to determine how many seconds it will take for the tank to fill, we must divide the volume by the rate of flow of the water.

time in seconds = (πr2)/(3w)

In order to convert from seconds to minutes, we must divide the number of seconds by sixty. Dividing by sixty is the same is multiplying by 1/60.

(πr2)/(3w) * (1/60) = π(r2)(h)/(180w)

The basic form for the volume of a cone is:

V = (1/3)πr_2_h

For this simple problem, we merely need to plug in our values:

V = (1/3)π_132 * 6 = 169 * 2_π = 338_π_ in3

There are two things to be careful with here. First, we must solve for the radius of the base. Secondly, note that the height is given in feet, not inches. Notice that all the answers are in cubic inches. Therefore, it will be easiest to convert all of our units to inches.

First, solve for the radius, recalling that C = 2_πr_, or, for our values 77_π_ = 2_πr_. Solving for r, we get r = 77/2 or r = 38.5.

The height, in inches, is 24.

The basic form for the volume of a cone is: V = (1 / 3)πr_2_h

For our values this would be:

V = (1/3)π * 38.52 * 24 = 8 * 1482.25_π_ = 11,858π in3

The general formula is given by V = 1/3Bh = 1/3pi $r^{2}$h, where = radius and = height.

The diameter is 6 cm, so the radius is 3 cm.

First we will calculate the volume of the cone

Next we will determine the time it will take to fill that volume

We will then convert that into minutes

The radius and the height of a cone are required in order to find its volume.

The radius is 50 centimeters, which can be converted to meters by dividing by 100:

meters

The slant height is 120 centimeters, which converts similarly to

meters

To find the height, we need to use the Pythagorean Theorem with the radius 0.5 as one leg and the slant height 1.2 as the hypotenuse of a right triangle, and the height as the other leg:

meters.

The volume formula can now be used:

cubic meters