Math / Geometry

QuestionFind the volume of the cone shown below. A. $392 \pi$ units $^{3}$ B. $1176 \pi$ units $^{3}$ C. 1176 units $^{3}$ D. 392 units $^{3}$

Studdy Solution

STEP 1

What is this asking? We need to find how much space this cone takes up, given its height and the size of its circular base! Watch out! Don't mix up the formulas for volume and surface area!
Also, keep an eye on those $\pi$ s in the answer choices!

STEP 2

1. Recall the formula
2. Plug and chug
3. Simplify

STEP 3

Alright, let's kick things off with the formula for the volume of a cone.
It's $V = \frac{1}{3} \cdot \pi \cdot r^2 \cdot h$ , where $V$ is the volume, $r$ is the radius of the circular base, and $h$ is the height of the cone.
Remember, it's like a pyramid but with a circle on the bottom!

STEP 4

Now, let's plug in the values we know!
We're given that the radius $r$ is $\textbf{7}$ units and the height $h$ is $\textbf{24}$ units.
So, we have $V = \frac{1}{3} \cdot \pi \cdot (\textbf{7})^2 \cdot (\textbf{24})$ .

STEP 5

Time to simplify!
First, let's square the radius: $7^2 = 7 \cdot 7 = \textbf{49}$ .
So, our formula becomes $V = \frac{1}{3} \cdot \pi \cdot \textbf{49} \cdot 24$ .

STEP 6

Now, we can multiply $49$ and $24$ : $49 \cdot 24 = \textbf{1176}$ .
So, we have $V = \frac{1}{3} \cdot \pi \cdot \textbf{1176}$ .

STEP 7

Finally, let's multiply by $\frac{1}{3}$ , which is the same as dividing by $3$ : $\frac{1176}{3} = \textbf{392}$ .
So, our final volume is $V = \textbf{392}\pi$ cubic units.

STEP 8

The volume of the cone is $392\pi$ cubic units, which matches answer choice A!

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QuestionFind the volume of the cone shown below. A. $392 \pi$ units $^{3}$ B. $1176 \pi$ units $^{3}$ C. 1176 units $^{3}$ D. 392 units $^{3}$

Studdy Solution

STEP 1

What is this asking? We need to find how much space this cone takes up, given its height and the size of its circular base! Watch out! Don't mix up the formulas for volume and surface area!
Also, keep an eye on those $\pi$ s in the answer choices!

STEP 2

1. Recall the formula
2. Plug and chug
3. Simplify

STEP 3

Alright, let's kick things off with the formula for the volume of a cone.
It's $V = \frac{1}{3} \cdot \pi \cdot r^2 \cdot h$ , where $V$ is the volume, $r$ is the radius of the circular base, and $h$ is the height of the cone.
Remember, it's like a pyramid but with a circle on the bottom!

STEP 4

Now, let's plug in the values we know!
We're given that the radius $r$ is $\textbf{7}$ units and the height $h$ is $\textbf{24}$ units.
So, we have $V = \frac{1}{3} \cdot \pi \cdot (\textbf{7})^2 \cdot (\textbf{24})$ .

STEP 5

Time to simplify!
First, let's square the radius: $7^2 = 7 \cdot 7 = \textbf{49}$ .
So, our formula becomes $V = \frac{1}{3} \cdot \pi \cdot \textbf{49} \cdot 24$ .

STEP 6

Now, we can multiply $49$ and $24$ : $49 \cdot 24 = \textbf{1176}$ .
So, we have $V = \frac{1}{3} \cdot \pi \cdot \textbf{1176}$ .

STEP 7

Finally, let's multiply by $\frac{1}{3}$ , which is the same as dividing by $3$ : $\frac{1176}{3} = \textbf{392}$ .
So, our final volume is $V = \textbf{392}\pi$ cubic units.

STEP 8

The volume of the cone is $392\pi$ cubic units, which matches answer choice A!

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QuestionFind the volume of the cone shown below. A. 392π392 \pi392π units 3^{3}3 B. 1176π1176 \pi1176π units 3^{3}3 C. 1176 units 3^{3}3 D. 392 units 3^{3}3

Studdy Solution

STEP 1

What is this asking? We need to find how much space this cone takes up, given its height and the size of its circular base! Watch out! Don't mix up the formulas for volume and surface area!Also, keep an eye on those π\piπs in the answer choices!

STEP 2

1. Recall the formula2. Plug and chug3. Simplify

STEP 3

STEP 4

Now, let's **plug in** the values we know!We're given that the **radius** rrr is 7\textbf{7}7 units and the **height** hhh is 24\textbf{24}24 units.So, we have V=13⋅π⋅(7)2⋅(24)V = \frac{1}{3} \cdot \pi \cdot (\textbf{7})^2 \cdot (\textbf{24})V=31​⋅π⋅(7)2⋅(24).

STEP 5

Time to **simplify**!First, let's square the radius: 72=7⋅7=497^2 = 7 \cdot 7 = \textbf{49}72=7⋅7=49.So, our formula becomes V=13⋅π⋅49⋅24V = \frac{1}{3} \cdot \pi \cdot \textbf{49} \cdot 24V=31​⋅π⋅49⋅24.

STEP 6

Now, we can multiply 494949 and 242424: 49⋅24=117649 \cdot 24 = \textbf{1176}49⋅24=1176.So, we have V=13⋅π⋅1176V = \frac{1}{3} \cdot \pi \cdot \textbf{1176}V=31​⋅π⋅1176.

STEP 7

Finally, let's multiply by 13\frac{1}{3}31​, which is the same as dividing by 333: 11763=392\frac{1176}{3} = \textbf{392}31176​=392.So, our **final volume** is V=392πV = \textbf{392}\piV=392π cubic units.

STEP 8

The volume of the cone is 392π392\pi392π cubic units, which matches answer choice A!

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the volume of the cone shown below. A. $392 \pi$ units $^{3}$ B. $1176 \pi$ units $^{3}$ C. 1176 units $^{3}$ D. 392 units $^{3}$

What is this asking? We need to find how much space this cone takes up, given its height and the size of its circular base! Watch out! Don't mix up the formulas for volume and surface area!
Also, keep an eye on those $\pi$ s in the answer choices!

1. Recall the formula
2. Plug and chug
3. Simplify

Now, let's plug in the values we know!
We're given that the radius $r$ is $\textbf{7}$ units and the height $h$ is $\textbf{24}$ units.
So, we have $V = \frac{1}{3} \cdot \pi \cdot (\textbf{7})^2 \cdot (\textbf{24})$ .

Time to simplify!
First, let's square the radius: $7^2 = 7 \cdot 7 = \textbf{49}$ .
So, our formula becomes $V = \frac{1}{3} \cdot \pi \cdot \textbf{49} \cdot 24$ .

Now, we can multiply $49$ and $24$ : $49 \cdot 24 = \textbf{1176}$ .
So, we have $V = \frac{1}{3} \cdot \pi \cdot \textbf{1176}$ .

Finally, let's multiply by $\frac{1}{3}$ , which is the same as dividing by $3$ : $\frac{1176}{3} = \textbf{392}$ .
So, our final volume is $V = \textbf{392}\pi$ cubic units.

The volume of the cone is $392\pi$ cubic units, which matches answer choice A!