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Intermediate Geometry : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1143 : Intermediate Geometry

Find the volume of the prism.

Possible Answers:

7000

7200

6600

6800

Correct answer:

6600

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.

$\text{Area of Trapezoid}=\frac{20+24}{2}(10)=220$

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

$\text{Volume of Prism}=220\times 30 =6600$

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Example Question #1144 : Intermediate Geometry

Find the volume of the prism.

Possible Answers:

4500

3600

4200

3900

Correct answer:

4200

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.

$\text{Area of Trapezoid}=\frac{4+24}{2}(10)=140$

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

$\text{Volume of Prism}=140\times 30 =4200$

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Example Question #1145 : Intermediate Geometry

Find the volume of the prism.

Possible Answers:

4701

4901

4601

4801

Correct answer:

4901

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.

$\text{Area of Trapezoid}=\frac{9+17}{2}(13)=169$

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

$\text{Volume of Prism}=169\times 29 =4901$

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Example Question #1146 : Intermediate Geometry

Find the volume of the prism.

Possible Answers:

15554

14992

15488

16002

Correct answer:

15488

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.

$\text{Area of Trapezoid}=\frac{19+25}{2}(22)=484$

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

$\text{Volume of Prism}=484\times 32 =15488$

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Example Question #1147 : Intermediate Geometry

Find the volume of the prism.

Possible Answers:

Correct answer:

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.

$\text{Area of Trapezoid}=\frac{1+3}{2}(5)=10$

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

$\text{Volume of Prism}=10\times 7 =70$

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Example Question #1148 : Intermediate Geometry

Find the volume of the regular hexagonal prism.

Possible Answers:

1998.55

1999.76

1995.32

1991.32

Correct answer:

1995.32

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.

$\text{Volume of Prism}=96\sqrt3 \times 12=1152\sqrt3=1995.32$

Remember to round to places after the decimal.

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Example Question #1149 : Intermediate Geometry

Find the volume of the regular hexagonal prism.

Possible Answers:

101.23

99.54

103.92

97.55

Correct answer:

103.92

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.

$\text{Area of Base}=\frac{3\sqrt3}{2}(2)^2=6\sqrt3$

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

$\text{Volume of Prism}=6\sqrt3 \times 10=60\sqrt3=103.92$

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:

2299.41

2327.88

2401.21

2329.05

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 #32 : How To Find The Volume Of A Prism

Find the volume of the regular hexagonal prism.

Possible Answers:

8661.25

8109.59

8225.69

8342.42

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.

Report an Error

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

Find the volume of the regular hexagonal prism.

Possible Answers:

169.29

163.68

162.70

151.40

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.

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Intermediate Geometry : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1143 : Intermediate Geometry

Example Question #1144 : Intermediate Geometry

Example Question #1145 : Intermediate Geometry

Example Question #1146 : Intermediate Geometry

Example Question #1147 : Intermediate Geometry

Example Question #1148 : Intermediate Geometry

Example Question #1149 : Intermediate Geometry

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

Example Question #32 : How To Find The Volume Of A Prism

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

All Intermediate Geometry Resources

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