I don’t understand this, how would I solve this? **Volume of a Grain Silo**A grain silo can be modeled as a right cylinder topped with a hemisphere. Find the volume of the silo if it has a height of 48 m and a radius of 9 m. Round your answer to the nearest tenth if necessary. (Note: diagram is not drawn to scale.)**Diagram Explanation:**The diagram consists of a right cylinder with a hemispherical top. The cylinder has a height of 48 meters and a radius of 9 meters. The radius is consistent for both the cylindrical part and the hemispherical top.**Solution:**To find the total volume of the grain silo, we need to sum the volume of the cylindrical part and the volume of the hemispherical top.1. **Volume of the Cylinder:** The volume \(V_{cylinder}\) of a cylinder is calculated using the formula: \[ V_{cylinder} = \pi r^2 h \] - \(r\) is the radius (9 m) - \(h\) is the height (48 m) \[ V_{cylinder} = \pi (9^2)(48) = \pi (81)(48) = 3888\pi \, \text{m}^3 \]2. **Volume of the Hemisphere:** The volume \(V_{hemisphere}\) of a hemisphere is calculated as half the volume of a sphere, using the formula: \[ V_{hemisphere} = \frac{1}{2} \left( \frac{4}{3}\pi r^3 \right) = \frac{2}{3}\pi r^3 \] - \(r\) is the radius (9 m) \[ V_{hemisphere} = \frac{2}{3} \pi (9^3) = \frac{2}{3} \pi (729) = 486\pi \, \text{m}^3 \]3. **Total Volume:** The total volume \(V_{total}\) of the silo is the sum of the volumes of the cylinder and the hemisphere: \[ V_{total} = V_{cylinder} + V_{hemisphere} = 3888\pi + 486\pi = 4374\pi \, \text{m}

A grain silo can be modeled as a right cylinder topped with a hemisphere. Find the volume of the silo if it has a height of 48 m and a radius of 9 m. Round your answer to the nearest tenth if necessary. (Note: diagram is not drawn to scale.) 48 9

A grain silo can be modeled as a right cylinder topped with a hemisphere. Find the volume of the silo if it has a height of 48 m and a radius of 9 m. Round your answer to the nearest tenth if necessary. (Note: diagram is not drawn to scale.) 48 9

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

I don’t understand this, how would I solve this?

**Volume of a Grain Silo**

A grain silo can be modeled as a right cylinder topped with a hemisphere. Find the volume of the silo if it has a height of 48 m and a radius of 9 m. Round your answer to the nearest tenth if necessary. (Note: diagram is not drawn to scale.)

**Diagram Explanation:**

The diagram consists of a right cylinder with a hemispherical top. The cylinder has a height of 48 meters and a radius of 9 meters. The radius is consistent for both the cylindrical part and the hemispherical top.

**Solution:**

To find the total volume of the grain silo, we need to sum the volume of the cylindrical part and the volume of the hemispherical top.

1. **Volume of the Cylinder:**
The volume \(V_{cylinder}\) of a cylinder is calculated using the formula:
\[
V_{cylinder} = \pi r^2 h
\]
- \(r\) is the radius (9 m)
- \(h\) is the height (48 m)
\[
V_{cylinder} = \pi (9^2)(48) = \pi (81)(48) = 3888\pi \, \text{m}^3
\]

2. **Volume of the Hemisphere:**
The volume \(V_{hemisphere}\) of a hemisphere is calculated as half the volume of a sphere, using the formula:
\[
V_{hemisphere} = \frac{1}{2} \left( \frac{4}{3}\pi r^3 \right) = \frac{2}{3}\pi r^3
\]
- \(r\) is the radius (9 m)
\[
V_{hemisphere} = \frac{2}{3} \pi (9^3) = \frac{2}{3} \pi (729) = 486\pi \, \text{m}^3
\]

3. **Total Volume:**
The total volume \(V_{total}\) of the silo is the sum of the volumes of the cylinder and the hemisphere:
\[
V_{total} = V_{cylinder} + V_{hemisphere} = 3888\pi + 486\pi = 4374\pi \, \text{m}

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