QuestionA farmer's tank has a cone on top with a radius of $10 \mathrm{~m}$ and height $2 \mathrm{~m}$ , plus a $5 \mathrm{~m}$ cylinder. Find the cone's volume.

Studdy Solution

STEP 1

Assumptions1. The base of the cone has a radius of10 m. The perpendicular height of the cone is m3. The formula for the volume of a cone is given by $\frac{1}{3}\pi r^ h$ , where $r$ is the radius of the base, $h$ is the height, and $\pi$ is a constant approximately equal to3.14159

STEP 2

We need to find the volume of the cone. We can do this by substituting the given values into the formula for the volume of a cone.
$V_{cone} = \frac{1}{}\pi r^2 h$

STEP 3

Now, plug in the given values for the radius and height of the cone to calculate the volume.
$V_{cone} = \frac{1}{3}\pi (10 m)^2 (2 m)$

STEP 4

Calculate the square of the radius.
$(10 m)^2 =100 m^2$ So, the volume of the cone becomes $V_{cone} = \frac{1}{3}\pi (100 m^2) (2 m)$

STEP 5

Calculate the volume of the cone.
$V_{cone} = \frac{1}{3}\pi (100 m^2) (2 m) = \frac{2}{3}\pi (100 m^2) = \frac{200}{3}\pi m^3$ The volume of the cone is $\frac{200}{3}\pi m^3$ .

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QuestionA farmer's tank has a cone on top with a radius of $10 \mathrm{~m}$ and height $2 \mathrm{~m}$ , plus a $5 \mathrm{~m}$ cylinder. Find the cone's volume.

Studdy Solution

STEP 1

Assumptions1. The base of the cone has a radius of10 m. The perpendicular height of the cone is m3. The formula for the volume of a cone is given by $\frac{1}{3}\pi r^ h$ , where $r$ is the radius of the base, $h$ is the height, and $\pi$ is a constant approximately equal to3.14159

STEP 2

We need to find the volume of the cone. We can do this by substituting the given values into the formula for the volume of a cone.
$V_{cone} = \frac{1}{}\pi r^2 h$

STEP 3

Now, plug in the given values for the radius and height of the cone to calculate the volume.
$V_{cone} = \frac{1}{3}\pi (10 m)^2 (2 m)$

STEP 4

Calculate the square of the radius.
$(10 m)^2 =100 m^2$ So, the volume of the cone becomes $V_{cone} = \frac{1}{3}\pi (100 m^2) (2 m)$

STEP 5

Calculate the volume of the cone.
$V_{cone} = \frac{1}{3}\pi (100 m^2) (2 m) = \frac{2}{3}\pi (100 m^2) = \frac{200}{3}\pi m^3$ The volume of the cone is $\frac{200}{3}\pi m^3$ .

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QuestionA farmer's tank has a cone on top with a radius of 10 m10 \mathrm{~m}10 m and height 2 m2 \mathrm{~m}2 m, plus a 5 m5 \mathrm{~m}5 m cylinder. Find the cone's volume.

Studdy Solution

STEP 1

Assumptions1. The base of the cone has a radius of10 m. The perpendicular height of the cone is m3. The formula for the volume of a cone is given by 13πrh\frac{1}{3}\pi r^ h31​πrh, where rrr is the radius of the base, hhh is the height, and π\piπ is a constant approximately equal to3.14159

STEP 2

We need to find the volume of the cone. We can do this by substituting the given values into the formula for the volume of a cone.Vcone=1πr2hV_{cone} = \frac{1}{}\pi r^2 hVcone​=1​πr2h

STEP 3

Now, plug in the given values for the radius and height of the cone to calculate the volume.Vcone=13π(10m)2(2m)V_{cone} = \frac{1}{3}\pi (10 m)^2 (2 m)Vcone​=31​π(10m)2(2m)

STEP 4

Calculate the square of the radius.(10m)2=100m2(10 m)^2 =100 m^2(10m)2=100m2So, the volume of the cone becomesVcone=13π(100m2)(2m)V_{cone} = \frac{1}{3}\pi (100 m^2) (2 m)Vcone​=31​π(100m2)(2m)

STEP 5

Calculate the volume of the cone.Vcone=13π(100m2)(2m)=23π(100m2)=2003πm3V_{cone} = \frac{1}{3}\pi (100 m^2) (2 m) = \frac{2}{3}\pi (100 m^2) = \frac{200}{3}\pi m^3Vcone​=31​π(100m2)(2m)=32​π(100m2)=3200​πm3The volume of the cone is 2003πm3\frac{200}{3}\pi m^33200​πm3.

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QuestionA farmer's tank has a cone on top with a radius of $10 \mathrm{~m}$ and height $2 \mathrm{~m}$ , plus a $5 \mathrm{~m}$ cylinder. Find the cone's volume.

Assumptions1. The base of the cone has a radius of10 m. The perpendicular height of the cone is m3. The formula for the volume of a cone is given by $\frac{1}{3}\pi r^ h$ , where $r$ is the radius of the base, $h$ is the height, and $\pi$ is a constant approximately equal to3.14159

We need to find the volume of the cone. We can do this by substituting the given values into the formula for the volume of a cone.
$V_{cone} = \frac{1}{}\pi r^2 h$

Now, plug in the given values for the radius and height of the cone to calculate the volume.
$V_{cone} = \frac{1}{3}\pi (10 m)^2 (2 m)$

Calculate the square of the radius.
$(10 m)^2 =100 m^2$ So, the volume of the cone becomes $V_{cone} = \frac{1}{3}\pi (100 m^2) (2 m)$

Calculate the volume of the cone.
$V_{cone} = \frac{1}{3}\pi (100 m^2) (2 m) = \frac{2}{3}\pi (100 m^2) = \frac{200}{3}\pi m^3$ The volume of the cone is $\frac{200}{3}\pi m^3$ .