Math / Geometry

QuestionWhich is closest to the volume of the figure shown? $922.1 \mathrm{~m}^{3}$ $1,590.9 \mathrm{~m}^{3}$ $2,766.4 \mathrm{~m}^{3}$ $4,772.8 \mathrm{~m}^{3}$

Studdy Solution

STEP 1

What is this asking? We need to find the volume of a cone, given its height and radius. Watch out! Don't confuse the slant height with the actual height of the cone, and don't mix up the formulas for volume and surface area!

STEP 2

1. Recall the formula
2. Plug in the values
3. Calculate the volume

STEP 3

Alright, let's kick things off!
The volume $V$ of a cone is given by the super cool formula: $V = \frac{1}{3} \cdot \pi \cdot r^2 \cdot h$ , where $r$ is the radius of the circular base and $h$ is the perpendicular height from the base to the tip-top of the cone.
This formula is like a secret code to unlock the cone's volume!

STEP 4

Now, let's plug in our given values.
We have $r = 10$ meters and $h = 15.2$ meters.
Notice that we're given the slant height too, but we don't need it for the volume.
That's a sneaky trick to see if you're paying attention!
So, substituting these values into our formula, we get: $V = \frac{1}{3} \cdot \pi \cdot (10)^2 \cdot 15.2$ .

STEP 5

Time to crunch some numbers!
First, let's square the radius: $(10)^2 = 100$ .
So now we have $V = \frac{1}{3} \cdot \pi \cdot 100 \cdot 15.2$ .

STEP 6

Now, let's multiply $100$ by $15.2$ to get $1520$ .
So, $V = \frac{1}{3} \cdot \pi \cdot 1520$ .

STEP 7

Next, let's multiply $1520$ by $\frac{1}{3}$ to get approximately $506.67$ .
So, $V \approx 506.67 \cdot \pi$ .

STEP 8

Finally, multiplying by $\pi$ (approximately $3.14159$ ), we get $V \approx 506.67 \cdot 3.14159 \approx 1590.87$ .
So, our final volume is approximately $1590.87$ cubic meters.

STEP 9

The closest answer is $1,590.9 \mathrm{~m}^{3}$ .
We nailed it!

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QuestionWhich is closest to the volume of the figure shown? $922.1 \mathrm{~m}^{3}$ $1,590.9 \mathrm{~m}^{3}$ $2,766.4 \mathrm{~m}^{3}$ $4,772.8 \mathrm{~m}^{3}$

Studdy Solution

STEP 1

What is this asking? We need to find the volume of a cone, given its height and radius. Watch out! Don't confuse the slant height with the actual height of the cone, and don't mix up the formulas for volume and surface area!

STEP 2

1. Recall the formula
2. Plug in the values
3. Calculate the volume

STEP 3

STEP 4

STEP 5

Time to crunch some numbers!
First, let's square the radius: $(10)^2 = 100$ .
So now we have $V = \frac{1}{3} \cdot \pi \cdot 100 \cdot 15.2$ .

STEP 6

Now, let's multiply $100$ by $15.2$ to get $1520$ .
So, $V = \frac{1}{3} \cdot \pi \cdot 1520$ .

STEP 7

Next, let's multiply $1520$ by $\frac{1}{3}$ to get approximately $506.67$ .
So, $V \approx 506.67 \cdot \pi$ .

STEP 8

Finally, multiplying by $\pi$ (approximately $3.14159$ ), we get $V \approx 506.67 \cdot 3.14159 \approx 1590.87$ .
So, our final volume is approximately $1590.87$ cubic meters.

STEP 9

The closest answer is $1,590.9 \mathrm{~m}^{3}$ .
We nailed it!

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QuestionWhich is closest to the volume of the figure shown? 922.1 m3922.1 \mathrm{~m}^{3}922.1 m3 1,590.9 m31,590.9 \mathrm{~m}^{3}1,590.9 m3 2,766.4 m32,766.4 \mathrm{~m}^{3}2,766.4 m3 4,772.8 m34,772.8 \mathrm{~m}^{3}4,772.8 m3

Studdy Solution

STEP 1

What is this asking? We need to find the volume of a cone, given its height and radius. Watch out! Don't confuse the slant height with the actual height of the cone, and don't mix up the formulas for volume and surface area!

STEP 2

1. Recall the formula2. Plug in the values3. Calculate the volume

STEP 3

STEP 4

STEP 5

Time to **crunch some numbers**!First, let's square the radius: (10)2=100(10)^2 = 100(10)2=100.So now we have V=13⋅π⋅100⋅15.2V = \frac{1}{3} \cdot \pi \cdot 100 \cdot 15.2V=31​⋅π⋅100⋅15.2.

STEP 6

Now, let's multiply 100100100 by 15.215.215.2 to get 152015201520.So, V=13⋅π⋅1520V = \frac{1}{3} \cdot \pi \cdot 1520V=31​⋅π⋅1520.

STEP 7

Next, let's multiply 152015201520 by 13\frac{1}{3}31​ to get approximately 506.67506.67506.67.So, V≈506.67⋅πV \approx 506.67 \cdot \piV≈506.67⋅π.

STEP 8

Finally, multiplying by π\piπ (approximately 3.141593.141593.14159), we get V≈506.67⋅3.14159≈1590.87V \approx 506.67 \cdot 3.14159 \approx 1590.87V≈506.67⋅3.14159≈1590.87.So, our **final volume** is approximately 1590.871590.871590.87 cubic meters.

STEP 9

The closest answer is 1,590.9 m31,590.9 \mathrm{~m}^{3}1,590.9 m3.We nailed it!

Get Studdy

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.

QuestionWhich is closest to the volume of the figure shown? $922.1 \mathrm{~m}^{3}$ $1,590.9 \mathrm{~m}^{3}$ $2,766.4 \mathrm{~m}^{3}$ $4,772.8 \mathrm{~m}^{3}$

1. Recall the formula
2. Plug in the values
3. Calculate the volume

Time to crunch some numbers!
First, let's square the radius: $(10)^2 = 100$ .
So now we have $V = \frac{1}{3} \cdot \pi \cdot 100 \cdot 15.2$ .

Now, let's multiply $100$ by $15.2$ to get $1520$ .
So, $V = \frac{1}{3} \cdot \pi \cdot 1520$ .

Next, let's multiply $1520$ by $\frac{1}{3}$ to get approximately $506.67$ .
So, $V \approx 506.67 \cdot \pi$ .

Finally, multiplying by $\pi$ (approximately $3.14159$ ), we get $V \approx 506.67 \cdot 3.14159 \approx 1590.87$ .
So, our final volume is approximately $1590.87$ cubic meters.

The closest answer is $1,590.9 \mathrm{~m}^{3}$ .
We nailed it!