## Volume of a Pyramid Calculation**Problem Statement:**Find the volume of a pyramid with a square base, where the side length of the base is 13.9 cm and the height of the pyramid is 6.3 cm. Round your answer to the nearest tenth of a cubic centimeter.**Solution Steps:**1. **Formula for the Volume of a Pyramid:** The volume $ V $ of a pyramid is given by the formula: \[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]2. **Calculate the Base Area:** The base of the pyramid is a square. The area $ A $ of a square is calculated using the formula: \[ A = \text{side length}^2 \] Given that the side length of the base is 13.9 cm: \[ A = 13.9 \, \text{cm} \times 13.9 \, \text{cm} = 193.21 \, \text{cm}^2 \]3. **Calculate the Volume:** Substitute the base area and the height into the volume formula: \[ V = \frac{1}{3} \times 193.21 \, \text{cm}^2 \times 6.3 \, \text{cm} \] \[ V = \frac{1}{3} \times 1217.223 \, \text{cm}^3 \] \[ V \approx 405.7 \, \text{cm}^3 \]4. **Round the Answer:** We round 405.7 to the nearest tenth of a cubic centimeter.**Answer:**\[\boxed{405.7 \, \text{cm}^3}\]This completes the calculation for the volume of the pyramid based on the given dimensions.

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Find the volume of a pyramid with a square base, where the side length of the base is 13.9 cm and the height of the pyramid is 6.3 cm. Round your answer to the nearest tenth of a cubic centimeter.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

## Volume of a Pyramid Calculation

**Problem Statement:**
Find the volume of a pyramid with a square base, where the side length of the base is 13.9 cm and the height of the pyramid is 6.3 cm. Round your answer to the nearest tenth of a cubic centimeter.

**Solution Steps:**
1. **Formula for the Volume of a Pyramid:**
The volume $ V $ of a pyramid is given by the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

2. **Calculate the Base Area:**
The base of the pyramid is a square. The area $ A $ of a square is calculated using the formula:
\[
A = \text{side length}^2
\]
Given that the side length of the base is 13.9 cm:
\[
A = 13.9 \, \text{cm} \times 13.9 \, \text{cm} = 193.21 \, \text{cm}^2
\]

3. **Calculate the Volume:**
Substitute the base area and the height into the volume formula:
\[
V = \frac{1}{3} \times 193.21 \, \text{cm}^2 \times 6.3 \, \text{cm}
\]
\[
V = \frac{1}{3} \times 1217.223 \, \text{cm}^3
\]
\[
V \approx 405.7 \, \text{cm}^3
\]

4. **Round the Answer:**
We round 405.7 to the nearest tenth of a cubic centimeter.

**Answer:**
\[
\boxed{405.7 \, \text{cm}^3}
\]

This completes the calculation for the volume of the pyramid based on the given dimensions.

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