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Intermediate Geometry : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1161 : Intermediate Geometry

Find the volume of the prism.

Possible Answers:

240

160

200

120

Correct answer:

160

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.

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

$\text{Area of Triangle}=\frac{4\times10}{2}=20$

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

$\text{Volume of Prism}=20\times 8=160$

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Example Question #65 : Prisms

Find the volume of the prism.

Possible Answers:

179

198

170

207

Correct answer:

198

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.

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

$\text{Area of Triangle}=\frac{4\times 11}{2}=22$

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

$\text{Volume of Prism}=22\times 9=198$

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Example Question #66 : Prisms

Find the volume of the prism.

Possible Answers:

1050

1078

1022

1092

Correct answer:

1050

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.

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

$\text{Area of Triangle}=\frac{10\times 15}{2}=75$

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

$\text{Volume of Prism}=75\times 14=1050$

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Example Question #71 : Prisms

Find the volume of the prism.

Possible Answers:

1524

1508

1490

1496

Correct answer:

1496

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.

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

$\text{Area of Triangle}=\frac{8\times 17}{2}=68$

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

$\text{Volume of Prism}=68\times 22=1496$

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Example Question #1162 : Intermediate Geometry

Find the volume of the prism.

Possible Answers:

816

858

780

870

Correct answer:

780

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.

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

$\text{Area of Triangle}=\frac{8\times 13}{2}=52$

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

$\text{Volume of Prism}=52\times 15=780$

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Example Question #49 : How To Find The Volume Of A Prism

Find the volume of a prism.

Possible Answers:

4620

4860

4900

4740

Correct answer:

4860

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.

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

$\text{Area of Triangle}=\frac{12\times 30}{2}=180$

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

$\text{Volume of Prism}=180\times 27=4860$

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Example Question #50 : How To Find The Volume Of A Prism

Find the volume of the prism.

Possible Answers:

648

660

636

672

Correct answer:

672

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.

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

$\text{Area of Triangle}=\frac{8\times 12}{2}=48$

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

$\text{Volume of Prism}=48\times 14=672$

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Example Question #51 : How To Find The Volume Of A Prism

Find the volume of the prism.

Possible Answers:

1900

1886

912

1812

Correct answer:

912

Explanation:

Recall how to find the volume of any prism.

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

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

$\text{Area of Trapezoid}=\frac{base_1+base_2}{2}(\text{height})$

Plug in the given bases and height to find the area of the trapezoid.

$\text{Area of Trapezoid}=\frac{5+14}{2}(8)=76$

Now, plug this in to find the volume of the prism.

$\text{Volume of Prism}=76\times12 =912$

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Example Question #52 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Possible Answers:

4702.19

4509.17

4881.22

2314.89

Correct answer:

2314.89

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.

$\text{Area of Base}=\frac{3\sqrt3}{2}(9)^2=\frac{243\sqrt3}{2}$

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

$\text{Volume of Prism}=\frac{243\sqrt3}{2} \times 11=2314.89$

Remember to round to places after the decimal.

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Example Question #53 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Possible Answers:

5972.98

25002.20

5992.11

25669.70

Correct answer:

5972.98

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.

$\text{Area of Base}=\frac{3\sqrt3}{2}(11)^2=\frac{363\sqrt3}{2}$

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

$\text{Volume of Prism}=\frac{363\sqrt3}{2} \times 19=5972.98$

Remember to round to places after the decimal.

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Intermediate Geometry : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1161 : Intermediate Geometry

Example Question #65 : Prisms

Example Question #66 : Prisms

Example Question #71 : Prisms

Example Question #1162 : Intermediate Geometry

Example Question #49 : How To Find The Volume Of A Prism

Example Question #50 : How To Find The Volume Of A Prism

Example Question #51 : How To Find The Volume Of A Prism

Example Question #52 : How To Find The Volume Of A Prism

Example Question #53 : How To Find The Volume Of A Prism

All Intermediate Geometry Resources

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