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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 #33 : Prisms

Find the volume of the prism.

Possible Answers:

160 $\displaystyle 160$

$\displaystyle 80$

120 $\displaystyle 120$

200 $\displaystyle 200$

Correct answer:

120 $\displaystyle 120$

Explanation:

Recall how to find the volume of a prism:

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

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(3)(8)=12$ $\displaystyle \text{Area of Right Triangle Base}=\frac{1}{2}(3)(8)=12$

Now, find the volume of the prism.

$\text{Volume of Prism}=12\times 10=120$ $\displaystyle \text{Volume of Prism}=12\times 10=120$

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Example Question #12 : How To Find The Volume Of A Prism

Find the volume of the prism.

Possible Answers:

660 $\displaystyle 660$

630 $\displaystyle 630$

600 $\displaystyle 600$

690 $\displaystyle 690$

Correct answer:

630 $\displaystyle 630$

Explanation:

Recall how to find the volume of a prism:

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

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(9)(10)=45$ $\displaystyle \text{Area of Right Triangle Base}=\frac{1}{2}(9)(10)=45$

Now, find the volume of the prism.

$\text{Volume of Prism}=45\times 14=630$ $\displaystyle \text{Volume of Prism}=45\times 14=630$

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Example Question #31 : Prisms

Find the volume of the prism.

Possible Answers:

432 $\displaystyle 432$

420 $\displaystyle 420$

444 $\displaystyle 444$

408 $\displaystyle 408$

Correct answer:

420 $\displaystyle 420$

Explanation:

Recall how to find the volume of a prism:

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

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(7)(10)=35$ $\displaystyle \text{Area of Right Triangle Base}=\frac{1}{2}(7)(10)=35$

Now, find the volume of the prism.

$\text{Volume of Prism}=35\times 12=420$ $\displaystyle \text{Volume of Prism}=35\times 12=420$

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Example Question #1133 : Intermediate Geometry

Find the volume of the prism.

Possible Answers:

2918 $\displaystyle 2918$

2871 $\displaystyle 2871$

2456 $\displaystyle 2456$

2211 $\displaystyle 2211$

Correct answer:

2871 $\displaystyle 2871$

Explanation:

Recall how to find the volume of a prism:

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

Find the area of the base, which is a right triangle.

$\text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$ $\displaystyle \text{Area of Right Triangle}=\frac{1}{2}(\text{base}\times\text{height})$

$\text{Area of Right Triangle Base}=\frac{1}{2}(11)(18)=99$ $\displaystyle \text{Area of Right Triangle Base}=\frac{1}{2}(11)(18)=99$

Now, find the volume of the prism.

$\text{Volume of Prism}=99\times 29 =2871$ $\displaystyle \text{Volume of Prism}=99\times 29 =2871$

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Example Question #1131 : Intermediate Geometry

Find the volume of the prism.

Possible Answers:

396 $\displaystyle 396$

402 $\displaystyle 402$

294 $\displaystyle 294$

390 $\displaystyle 390$

Correct answer:

396 $\displaystyle 396$

Explanation:

Recall how to find the volume of any prism.

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

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

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

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

$\text{Area of Trapezoid}=\frac{3+8}{2}(12)=66$ $\displaystyle \text{Area of Trapezoid}=\frac{3+8}{2}(12)=66$

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

$\text{Volume of Prism}=66 \times 6 =396$ $\displaystyle \text{Volume of Prism}=66 \times 6 =396$

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Example Question #171 : Solid Geometry

Find the volume of the prism.

Possible Answers:

1320 $\displaystyle 1320$

780 $\displaystyle 780$

900 $\displaystyle 900$

660 $\displaystyle 660$

Correct answer:

660 $\displaystyle 660$

Explanation:

Recall how to find the volume of any prism.

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

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

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

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

$\text{Area of Trapezoid}=\frac{4+8}{2}(11)=66$ $\displaystyle \text{Area of Trapezoid}=\frac{4+8}{2}(11)=66$

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

$\text{Volume of Prism}=66 \times 10 =660$ $\displaystyle \text{Volume of Prism}=66 \times 10 =660$

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Example Question #41 : Prisms

Find the volume of the prism.

Possible Answers:

1338 $\displaystyle 1338$

1288 $\displaystyle 1288$

1344 $\displaystyle 1344$

1296 $\displaystyle 1296$

Correct answer:

1344 $\displaystyle 1344$

Explanation:

Recall how to find the volume of any prism.

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

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

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

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

$\text{Area of Trapezoid}=\frac{6+10}{2}(12)=96$ $\displaystyle \text{Area of Trapezoid}=\frac{6+10}{2}(12)=96$

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

$\text{Volume of Prism}=96\times14 =1344$ $\displaystyle \text{Volume of Prism}=96\times14 =1344$

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Example Question #21 : How To Find The Volume Of A Prism

Find the volume of the prism.

Possible Answers:

1728 $\displaystyle 1728$

1818 $\displaystyle 1818$

1706 $\displaystyle 1706$

1694 $\displaystyle 1694$

Correct answer:

1728 $\displaystyle 1728$

Explanation:

Recall how to find the volume of any prism.

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

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

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

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

$\text{Area of Trapezoid}=\frac{4+14}{2}(12)=108$ $\displaystyle \text{Area of Trapezoid}=\frac{4+14}{2}(12)=108$

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

$\text{Volume of Prism}=108\times 16 =1728$ $\displaystyle \text{Volume of Prism}=108\times 16 =1728$

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Example Question #41 : Prisms

Find the volume of the prism.

Possible Answers:

972 $\displaystyle 972$

900 $\displaystyle 900$

890 $\displaystyle 890$

920 $\displaystyle 920$

Correct answer:

972 $\displaystyle 972$

Explanation:

Recall how to find the volume of any prism.

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

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

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

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

$\text{Area of Trapezoid}=\frac{3+15}{2}(9)=81$ $\displaystyle \text{Area of Trapezoid}=\frac{3+15}{2}(9)=81$

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

$\text{Volume of Prism}=81\times 12 =972$ $\displaystyle \text{Volume of Prism}=81\times 12 =972$

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Example Question #1142 : Intermediate Geometry

Find the volume of the prism.

Possible Answers:

1900 $\displaystyle 1900$

1860 $\displaystyle 1860$

1890 $\displaystyle 1890$

1910 $\displaystyle 1910$

Correct answer:

1890 $\displaystyle 1890$

Explanation:

Recall how to find the volume of any prism.

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

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

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

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

$\text{Area of Trapezoid}=\frac{12+16}{2}(9)=126$ $\displaystyle \text{Area of Trapezoid}=\frac{12+16}{2}(9)=126$

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

$\text{Volume of Prism}=126\times 15 =1890$ $\displaystyle \text{Volume of Prism}=126\times 15 =1890$

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Intermediate Geometry : Solid Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #33 : Prisms

Example Question #12 : How To Find The Volume Of A Prism

Example Question #31 : Prisms

Example Question #1133 : Intermediate Geometry

Example Question #1131 : Intermediate Geometry

Example Question #171 : Solid Geometry

Example Question #41 : Prisms

Example Question #21 : How To Find The Volume Of A Prism

Example Question #41 : Prisms

Example Question #1142 : Intermediate Geometry

All Intermediate Geometry Resources

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