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Intermediate Geometry : Prisms

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #15 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

Possible Answers:

299.14

297.45

288.82

301.68

Correct answer:

299.14

Explanation:

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

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

Now, since we have two hexagons, we can multiply the area by to get the area of both bases.

$\text{Area of Bases}=3\sqrt3(\text{side})^2$

Next, this prism has rectangles that make up its sides.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by to find the total area of all of the sides of the prism.

$\text{Area of Prism Sides}=6(\text{side})(\text{height})$

Add together the area of the sides and of the bases to find the surface area of the prism.

$\text{Surface Area of Prism}=\text{Area of Bases}+\text{Area of Sides}$

$\text{Surface Area of Prism}=3\sqrt3(\text{side})^2+6(\text{side})(\text{height})$

Plug in the given values to find the surface area of the prism.

$\text{Surface Area of Prism}=3\sqrt3(4)^2+6(4)(9)=299.14$

Make sure to round to places after the decimal.

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Example Question #16 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

Possible Answers:

5432.62

5596.87

5698.30

5678.46

Correct answer:

5678.46

Explanation:

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

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

Now, since we have two hexagons, we can multiply the area by to get the area of both bases.

$\text{Area of Bases}=3\sqrt3(\text{side})^2$

Next, this prism has rectangles that make up its sides.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by to find the total area of all of the sides of the prism.

$\text{Area of Prism Sides}=6(\text{side})(\text{height})$

Add together the area of the sides and of the bases to find the surface area of the prism.

$\text{Surface Area of Prism}=\text{Area of Bases}+\text{Area of Sides}$

$\text{Surface Area of Prism}=3\sqrt3(\text{side})^2+6(\text{side})(\text{height})$

Plug in the given values to find the surface area of the prism.

$\text{Surface Area of Prism}=3\sqrt3(20)^2+6(20)(30)=5678.46$

Make sure to round to places after the decimal.

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Example Question #11 : How To Find The Surface Area Of A Prism

Find the surface area of the regular hexagonal prism.

Possible Answers:

95.39

94.06

92.78

90.92

Correct answer:

92.78

Explanation:

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

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

Now, since we have two hexagons, we can multiply the area by to get the area of both bases.

$\text{Area of Bases}=3\sqrt3(\text{side})^2$

Next, this prism has rectangles that make up its sides.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by to find the total area of all of the sides of the prism.

$\text{Area of Prism Sides}=6(\text{side})(\text{height})$

Add together the area of the sides and of the bases to find the surface area of the prism.

$\text{Surface Area of Prism}=\text{Area of Bases}+\text{Area of Sides}$

$\text{Surface Area of Prism}=3\sqrt3(\text{side})^2+6(\text{side})(\text{height})$

Plug in the given values to find the surface area of the prism.

$\text{Surface Area of Prism}=3\sqrt3(2)^2+6(2)(6)=92.78$

Make sure to round to places after the decimal.

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

Find the surface area of the regular hexagonal prism.

Possible Answers:

4275.55

3596.62

2236.09

3667.88

Correct answer:

4275.55

Explanation:

In order to find the surface area, you will need to add up the areas of each face of the prism.

This hexagonal prism has two regular hexagons as its bases.

Recall how to find the area of a regular hexagon:

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

Now, since we have two hexagons, we can multiply the area by to get the area of both bases.

$\text{Area of Bases}=3\sqrt3(\text{side})^2$

Next, this prism has rectangles that make up its sides.

Recall how to find the area of a rectangle:

$\text{Area of Rectangle}=\text{length}\times\text{width}$

In this prism, the length is also the side of the hexagon, and the width of the rectangle is the height of the prism.

Now, multiply the area of the rectangle by to find the total area of all of the sides of the prism.

$\text{Area of Prism Sides}=6(\text{side})(\text{height})$

Add together the area of the sides and of the bases to find the surface area of the prism.

$\text{Surface Area of Prism}=\text{Area of Bases}+\text{Area of Sides}$

$\text{Surface Area of Prism}=3\sqrt3(\text{side})^2+6(\text{side})(\text{height})$

Plug in the given values to find the surface area of the prism.

$\text{Surface Area of Prism}=3\sqrt3(18)^2+6(18)(24)=4275.55$

Make sure to round to places after the decimal.

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Example Question #2 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

A prism with a square base has a height of feet.

If the edge of the base is feet, what is the volume of the prism?

Possible Answers:

$8\, ft^3$

$16\, ft^3$

$4\, ft^3$

$6\, ft^3$

Correct answer:

$16\, ft^3$

Explanation:

The volume of a prism is given as

V = Bh

where

B = Area of the base

and

h = height of the prism.

Because the base is a square, we have

B = s^2 = 2^2 = 4

So plugging in the value of B that we found and h that was given in the problem we get the volume to be the following.

$V = 4\cdot4 = 16\,ft^3$

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Example Question #2 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

A rectangular prism has the dimensions of $2\:in$ , $5\:in$ , and $7\:in$ . What is the volume of the prism?

Possible Answers:

$70\:in^2$

$72\:in^3$

$63 \:in^2$

$63\: in^3$

$70\:in^3$

Correct answer:

$70\:in^3$

Explanation:

The volume of a rectangular prism is given by the following equation:

$V= l \cdot w \cdot h$

In this equation, is length, is width, and is height.

The given information does not explicitly state which side each dimension measurement correlates to on the prism. Volume simply requires the multiplication of the dimensions together.

Volume can be solved for in the following way:

$V = 2\:in \cdot 5\:in \cdot 7\:in$

$V = 10\:in^2 \cdot 7\:in$

$V= 70 \:in^3$

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Example Question #3 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Find the volume of a rectangular prism with a width of $2\:cm$ , height of $8\:cm$ and length of $3\:cm$ .

Possible Answers:

$48\:cm^3$

$58\:cm^3$

$26\:cm^3$

$24\:cm^3$

$56\:cm^3$

Correct answer:

$48\:cm^3$

Explanation:

The volume of a rectangular prism is given by the following equation:

$V= l \cdot w \cdot h$

In this equation, is length, is width, and is height.

Because all the necessary information has been provided to solve for the volume, all that needs to be done is substituting in the values for the variables.

Therefore:

$V = 2\:cm \cdot 3\:cm \cdot 8\:cm$

$V = 6\:cm^2 \cdot 8\:cm$

$V = 48\:cm^3$

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Example Question #3 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Find the surface area of the rectangular prism:

Volume_of_a_prism

Possible Answers:

$453\:units^3$

$418\:units^3$

$468\:units^3$

$468\:units^2$

$410\:units^2$

Correct answer:

$410\:units^2$

Explanation:

The surface area of a rectangular prism is

SA=2lw+2lh+2wh

Substituting in the given information for this particular rectangular prism.

$\\SA=2(13\cdot 9)+2(13\cdot 4)+2(9\cdot 4) \\SA=410\ \text{units}^2$

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Example Question #4 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

A small rectangular fish tank has sides that are 18in wide, 30in long, and 24in high. Which formula would not work to find the correct volume of the fish tank?

Possible Answers:

$(24 \times 18) \times 30$

$(18 \times 30) + 24$

$(30 \times 24) \times 18$

$30 \times 432$

$720 \times 18$

Correct answer:

$(18 \times 30) + 24$

Explanation:

In this question the formula that uses addition will not yield the correct volume of the fish tank:

(18 x 30) + 24

This is the correct answer because in order to find the volume of any rectangular prism one needs to multiply the prism's length, width, and height together.

The volume of a rectangular prism is given by the following equation:

$V= l \cdot w \cdot h$

In this equation, is length, is width, and is height.

To restate, (18 x 30) + 24 is the correct answer because it will NOT yield the correct volume, you would need to multiply by the product of and , not add.

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Example Question #1 : How To Find The Volume Of A Prism

Find the volume of the prism.

Possible Answers:

1880

1720

1800

1960

Correct answer:

1800

Explanation:

Recall how to find the volume of a prism:

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

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

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

$\text{Area of Right Triangle Base}=\frac{1}{2}(12)(15)=90$

Now, find the volume of the prism.

$\text{Volume of Prism}=90 \times 20 =1800$

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Intermediate Geometry : Prisms

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #15 : How To Find The Surface Area Of A Prism

Example Question #16 : How To Find The Surface Area Of A Prism

Example Question #11 : How To Find The Surface Area Of A Prism

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

Example Question #2 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Example Question #2 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Example Question #3 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Example Question #3 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Example Question #4 : Find The Volume Of A Right Rectangular Prism With Fractional Edge Lengths: Ccss.Math.Content.6.G.A.2

Example Question #1 : How To Find The Volume Of A Prism

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