Math / Geometry

QuestionQuestion Watch Video Show Examples
Find the volume of a pyramid with a square base, where the side length of the base is 4.6 m and the height of the pyramid is 7.2 m . Round your answer to the nearest tenth of a cubic meter.
Answer Attempt 4 out of 5 50.7 $\mathrm{m}^{3}$ Submit Answer

Studdy Solution

STEP 1

What is this asking? We need to find the volume of a pyramid with a square base, given the side length of the base and the pyramid's height. Watch out! Don't mix up the formulas for the volume of a pyramid and the volume of a prism!

STEP 2

1. Find the area of the square base.
2. Calculate the pyramid's volume.
3. Round to the nearest tenth.

STEP 3

Alright, let's start by finding the area of the square base.
We know the side length is $4.6$ m.
The area of a square is side length times side length, right?

STEP 4

So, the area of the base is $4.6 \text{ m} \cdot 4.6 \text{ m} = 21.16 \text{ m}^2$ .
Boom!

STEP 5

Now, the volume of a pyramid is $\frac{1}{3}$ times the area of the base times the height.
We just found the area of the base, which is $21.16 \text{ m}^2$ , and we know the height of the pyramid is $7.2$ m.

STEP 6

Let's plug those values into our formula: $\text{Volume} = \frac{1}{3} \cdot 21.16 \text{ m}^2 \cdot 7.2 \text{ m}$

STEP 7

Multiplying those together, we get: $\text{Volume} = \frac{1}{3} \cdot 152.352 \text{ m}^3$

STEP 8

Dividing by three gives us the volume: $\text{Volume} = 50.784 \text{ m}^3$

STEP 9

We're almost there!
We need to round our answer to the nearest tenth.
Our calculated volume is $50.784 \text{ m}^3$ .
The digit in the hundredths place is $8$ , which is greater than or equal to $5$ , so we round up.

STEP 10

Therefore, the rounded volume is $50.8 \text{ m}^3$ .
Fantastic!

STEP 11

The volume of the pyramid is approximately $50.8 \text{ m}^3$ .

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QuestionQuestion Watch Video Show Examples
Find the volume of a pyramid with a square base, where the side length of the base is 4.6 m and the height of the pyramid is 7.2 m . Round your answer to the nearest tenth of a cubic meter.
Answer Attempt 4 out of 5 50.7 $\mathrm{m}^{3}$ Submit Answer

Studdy Solution

STEP 1

What is this asking? We need to find the volume of a pyramid with a square base, given the side length of the base and the pyramid's height. Watch out! Don't mix up the formulas for the volume of a pyramid and the volume of a prism!

STEP 2

1. Find the area of the square base.
2. Calculate the pyramid's volume.
3. Round to the nearest tenth.

STEP 3

Alright, let's start by finding the area of the square base.
We know the side length is $4.6$ m.
The area of a square is side length times side length, right?

STEP 4

So, the area of the base is $4.6 \text{ m} \cdot 4.6 \text{ m} = 21.16 \text{ m}^2$ .
Boom!

STEP 5

Now, the volume of a pyramid is $\frac{1}{3}$ times the area of the base times the height.
We just found the area of the base, which is $21.16 \text{ m}^2$ , and we know the height of the pyramid is $7.2$ m.

STEP 6

Let's plug those values into our formula: $\text{Volume} = \frac{1}{3} \cdot 21.16 \text{ m}^2 \cdot 7.2 \text{ m}$

STEP 7

Multiplying those together, we get: $\text{Volume} = \frac{1}{3} \cdot 152.352 \text{ m}^3$

STEP 8

Dividing by three gives us the volume: $\text{Volume} = 50.784 \text{ m}^3$

STEP 9

We're almost there!
We need to round our answer to the nearest tenth.
Our calculated volume is $50.784 \text{ m}^3$ .
The digit in the hundredths place is $8$ , which is greater than or equal to $5$ , so we round up.

STEP 10

Therefore, the rounded volume is $50.8 \text{ m}^3$ .
Fantastic!

STEP 11

The volume of the pyramid is approximately $50.8 \text{ m}^3$ .

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QuestionQuestion Watch Video Show ExamplesFind the volume of a pyramid with a square base, where the side length of the base is 4.6 m and the height of the pyramid is 7.2 m . Round your answer to the nearest tenth of a cubic meter.Answer Attempt 4 out of 5 50.7 m3\mathrm{m}^{3}m3 Submit Answer

Studdy Solution

STEP 1

What is this asking? We need to find the volume of a pyramid with a square base, given the side length of the base and the pyramid's height. Watch out! Don't mix up the formulas for the volume of a pyramid and the volume of a prism!

STEP 2

1. Find the area of the square base.2. Calculate the pyramid's volume.3. Round to the nearest tenth.

STEP 3

Alright, let's **start** by finding the area of the square base.We know the **side length** is 4.64.64.6 m.The area of a square is side length times side length, right?

STEP 4

So, the **area of the base** is 4.6 m⋅4.6 m=21.16 m24.6 \text{ m} \cdot 4.6 \text{ m} = 21.16 \text{ m}^24.6 m⋅4.6 m=21.16 m2.Boom!

STEP 5

Now, the **volume of a pyramid** is 13\frac{1}{3}31​ times the area of the base times the height.We just found the **area of the base**, which is 21.16 m221.16 \text{ m}^221.16 m2, and we know the **height** of the pyramid is 7.27.27.2 m.

STEP 6

Let's plug those **values** into our formula: Volume=13⋅21.16 m2⋅7.2 m \text{Volume} = \frac{1}{3} \cdot 21.16 \text{ m}^2 \cdot 7.2 \text{ m} Volume=31​⋅21.16 m2⋅7.2 m

STEP 7

Multiplying those together, we get: Volume=13⋅152.352 m3 \text{Volume} = \frac{1}{3} \cdot 152.352 \text{ m}^3 Volume=31​⋅152.352 m3

STEP 8

Dividing by three gives us the **volume**: Volume=50.784 m3 \text{Volume} = 50.784 \text{ m}^3 Volume=50.784 m3

STEP 9

We're almost there!We need to round our answer to the nearest tenth.Our **calculated volume** is 50.784 m350.784 \text{ m}^350.784 m3.The digit in the hundredths place is 888, which is greater than or equal to 555, so we round up.

STEP 10

Therefore, the **rounded volume** is 50.8 m350.8 \text{ m}^350.8 m3.Fantastic!

STEP 11

The volume of the pyramid is approximately 50.8 m350.8 \text{ m}^350.8 m3.

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.

QuestionQuestion Watch Video Show Examples
Find the volume of a pyramid with a square base, where the side length of the base is 4.6 m and the height of the pyramid is 7.2 m . Round your answer to the nearest tenth of a cubic meter.
Answer Attempt 4 out of 5 50.7 $\mathrm{m}^{3}$ Submit Answer

1. Find the area of the square base.
2. Calculate the pyramid's volume.
3. Round to the nearest tenth.

Alright, let's start by finding the area of the square base.
We know the side length is $4.6$ m.
The area of a square is side length times side length, right?

So, the area of the base is $4.6 \text{ m} \cdot 4.6 \text{ m} = 21.16 \text{ m}^2$ .
Boom!

Now, the volume of a pyramid is $\frac{1}{3}$ times the area of the base times the height.
We just found the area of the base, which is $21.16 \text{ m}^2$ , and we know the height of the pyramid is $7.2$ m.

Let's plug those values into our formula: $\text{Volume} = \frac{1}{3} \cdot 21.16 \text{ m}^2 \cdot 7.2 \text{ m}$

Multiplying those together, we get: $\text{Volume} = \frac{1}{3} \cdot 152.352 \text{ m}^3$

Dividing by three gives us the volume: $\text{Volume} = 50.784 \text{ m}^3$

We're almost there!
We need to round our answer to the nearest tenth.
Our calculated volume is $50.784 \text{ m}^3$ .
The digit in the hundredths place is $8$ , which is greater than or equal to $5$ , so we round up.

Therefore, the rounded volume is $50.8 \text{ m}^3$ .
Fantastic!

The volume of the pyramid is approximately $50.8 \text{ m}^3$ .