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Intermediate Geometry : How to find the volume of a prism

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Example Question #1150 : Intermediate Geometry

Find the volume of the regular hexagonal prism.

Possible Answers:

2299.41

2327.88

2329.05

2401.21

Correct answer:

2327.88

Explanation:

Recall the formula to find the volume of any prism:

$\text{Volume of Prism}=\text{Area of base}\times \text{height}$

Since the base is a regular hexagon, recall how to find the area of a regular hexagon.

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side})^2$

Plug in the given side to find the area of the base.

$\text{Area of Base}=\frac{3\sqrt3}{2}(8)^2=96\sqrt3$

Next, plug in the area of the base and the height to find the volume of the prism.

$\text{Volume of Prism}=96\sqrt3 \times 14=1344\sqrt3=2327.88$

Remember to round to places after the decimal.

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Example Question #31 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Possible Answers:

8342.42

8109.59

8225.69

8661.25

Correct answer:

8342.42

Explanation:

Recall the formula to find the volume of any prism:

$\text{Volume of Prism}=\text{Area of base}\times \text{height}$

Since the base is a regular hexagon, recall how to find the area of a regular hexagon.

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side})^2$

Plug in the given side to find the area of the base.

$\text{Area of Base}=\frac{3\sqrt3}{2}(13)^2=\frac{507\sqrt3}{2}$

Next, plug in the area of the base and the height to find the volume of the prism.

$\text{Volume of Prism}=\frac{507\sqrt3}{2} \times 19=8342.42$

Remember to round to places after the decimal.

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Example Question #31 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Possible Answers:

151.40

163.68

162.70

169.29

Correct answer:

163.68

Explanation:

Recall the formula to find the volume of any prism:

$\text{Volume of Prism}=\text{Area of base}\times \text{height}$

Since the base is a regular hexagon, recall how to find the area of a regular hexagon.

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side})^2$

Plug in the given side to find the area of the base.

$\text{Area of Base}=\frac{3\sqrt3}{2}(3)^2=\frac{27\sqrt3}{2}$

Next, plug in the area of the base and the height to find the volume of the prism.

$\text{Volume of Prism}=\frac{27\sqrt3}{2} \times 7=163.68$

Remember to round to places after the decimal.

Report an Error

Example Question #33 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Possible Answers:

387.82

394.56

389.71

401.67

Correct answer:

389.71

Explanation:

Recall the formula to find the volume of any prism:

$\text{Volume of Prism}=\text{Area of base}\times \text{height}$

Since the base is a regular hexagon, recall how to find the area of a regular hexagon.

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side})^2$

Plug in the given side to find the area of the base.

$\text{Area of Base}=\frac{3\sqrt3}{2}(5)^2=\frac{75\sqrt3}{2}$

Next, plug in the area of the base and the height to find the volume of the prism.

$\text{Volume of Prism}=\frac{75\sqrt3}{2} \times 6=389.71$

Remember to round to places after the decimal.

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Example Question #34 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Possible Answers:

9.47

8.01

10.39

11.56

Correct answer:

10.39

Explanation:

Recall the formula to find the volume of any prism:

$\text{Volume of Prism}=\text{Area of base}\times \text{height}$

Since the base is a regular hexagon, recall how to find the area of a regular hexagon.

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side})^2$

Plug in the given side to find the area of the base.

$\text{Area of Base}=\frac{3\sqrt3}{2}(1)^2=\frac{3\sqrt3}{2}$

Next, plug in the area of the base and the height to find the volume of the prism.

$\text{Volume of Prism}=\frac{3\sqrt3}{2} \times 4=10.39$

Remember to round to places after the decimal.

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Example Question #35 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Possible Answers:

4667.35

4590.02

4809.44

4416.73

Correct answer:

4416.73

Explanation:

Recall the formula to find the volume of any prism:

$\text{Volume of Prism}=\text{Area of base}\times \text{height}$

Since the base is a regular hexagon, recall how to find the area of a regular hexagon.

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side})^2$

Plug in the given side to find the area of the base.

$\text{Area of Base}=\frac{3\sqrt3}{2}(10)^2=150\sqrt3$

Next, plug in the area of the base and the height to find the volume of the prism.

$\text{Volume of Prism}=150\sqrt3\times 17=4416.73$

Remember to round to places after the decimal.

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Example Question #36 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Possible Answers:

950.02

974.28

931.42

944.50

Correct answer:

974.28

Explanation:

Recall the formula to find the volume of any prism:

$\text{Volume of Prism}=\text{Area of base}\times \text{height}$

Since the base is a regular hexagon, recall how to find the area of a regular hexagon.

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side})^2$

Plug in the given side to find the area of the base.

$\text{Area of Base}=\frac{3\sqrt3}{2}(5)^2=\frac{75\sqrt3}{2}$

Next, plug in the area of the base and the height to find the volume of the prism.

$\text{Volume of Prism}=\frac{75\sqrt3}{2} \times 15=974.28$

Remember to round to places after the decimal.

Report an Error

Example Question #37 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Possible Answers:

8978.95

8888.73

9005.92

8822.20

Correct answer:

8978.95

Explanation:

Recall the formula to find the volume of any prism:

$\text{Volume of Prism}=\text{Area of base}\times \text{height}$

Since the base is a regular hexagon, recall how to find the area of a regular hexagon.

$\text{Area of Regular Hexagon}=\frac{3\sqrt3}{2}(\text{side})^2$

Plug in the given side to find the area of the base.

$\text{Area of Base}=\frac{3\sqrt3}{2}(12)^2=216\sqrt3$

Next, plug in the area of the base and the height to find the volume of the prism.

$\text{Volume of Prism}=216\sqrt3 \times 24=8978.95$

Remember to round to places after the decimal.

Report an Error

Example Question #38 : How To Find The Volume Of A Prism

Find the volume of the prism.

Possible Answers:

432

440

424

448

Correct answer:

432

Explanation:

To find the volume of the prism, use the following formula:

$\text{Volume of Prism}=\text{Area of Base}\times \text{height}$

Since the base of this prism is a triangle, find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times \text{height}}{2}$

$\text{Area of Triangle}=\frac{18 \times 4}{2}=36$

Now, plug in the area of the base and the height of the prism to find the volume.

$\text{Volume of Prism}=36 \times 12 =432$

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Example Question #39 : How To Find The Volume Of A Prism

Find the volume of the prism.

Possible Answers:

360

240

200

180

Correct answer:

180

Explanation:

To find the volume of the prism, use the following formula:

$\text{Volume of Prism}=\text{Area of Base}\times \text{height}$

Since the base of this prism is a triangle, find the area of a triangle.

$\text{Area of Triangle}=\frac{\text{base}\times \text{height}}{2}$

$\text{Area of Triangle}=\frac{12 \times 3}{2}=18$

Now, plug in the area of the base and the height of the prism to find the volume.

$\text{Volume of Prism}=18\times 10 =180$

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Intermediate Geometry : How to find the volume of a prism

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1150 : Intermediate Geometry

Example Question #31 : How To Find The Volume Of A Prism

Example Question #31 : How To Find The Volume Of A Prism

Example Question #33 : How To Find The Volume Of A Prism

Example Question #34 : How To Find The Volume Of A Prism

Example Question #35 : How To Find The Volume Of A Prism

Example Question #36 : How To Find The Volume Of A Prism

Example Question #37 : How To Find The Volume Of A Prism

Example Question #38 : How To Find The Volume Of A Prism

Example Question #39 : How To Find The Volume Of A Prism

All Intermediate Geometry Resources

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