Geometry Tutor Worksheet 17 Volume of Prisms …...What is the volume of this regular pentagonal...

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Geometry Tutor

Worksheet 17

Volume

of

Prisms and Pyramids


Geometry Tutor - Worksheet 17 – Volume of Prisms and Pyramids

1. What is the volume of a rectangular prism whose length is 9 m, width is 5 m,

and height is 12 m?

2. What is the volume of a rectangular prism whose length is 4.6 cm, width is

3.8 cm, and height is 1.4 cm?

3. What is the width of a rectangular prism whose volume is 216 m3 whose

length is 6 m, and height is 9 m?


4. What is the height of a rectangular prism whose volume is 672 cm3 whose

length is 12 cm, and width is 7 cm?

5. What is the volume of this rectangular prism?

6. What is the volume of this cubic prism?


7. What is the volume of this rectangular prism if 𝑈𝑉 = 9 mm, 𝑆𝑌 =

15 mm, and 𝑇𝑊 = 6 mm?

8. What is the volume of this triangular prism?


11. What is the volume of this rectangular prism if 𝐴𝐵 = 7 cm, 𝐵𝐶 =

11 cm, and 𝐶𝐺 = 14 cm?



13. What is the volume of this heptagonal prism if the area of the base is

140 mm2?



15. What is the volume of this regular pentagonal prism if the area of the base is

30 hm2?

16. What is the volume of a square pyramid measuring 13 m along each edge of

the base with a height of 12 m?

17. What is the volume of a pyramid that is 8 cm tall with a right triangle for a

base with sides 18 cm, 24 cm, and 30 cm?


18. What is the volume of this pyramid?




21. What is the volume of this pyramid if the area of the pentagonal base of the

pyramid is 249 cm2?


22. What is the volume of this pyramid if the area of the hexagonal base of the

pyramid is 93.6 m2?




pyramid is 139.5 dm2?



26. The volume of a square pyramid is 864 m3. The height of the pyramid is 18 m.

What is the length of the edges of the base?

27. The volume of a rectangular pyramid is 1080 cm3. What is the height of the

pyramid if the lengths of the edges of the base are 12 cm and 18 cm?

28. The volume of a square pyramid is 2048 mm3. What is the height of the

pyramid if the length of the edges of the base are 16 mm?


Answers - Geometry Tutor - Worksheet 17 – Volume of Prisms and Pyramids

1. What is the volume of a rectangular prism whose length is 9 m, width is 5 m,

and height is 12 m?

The formula for calculating the volume of a rectangular prism is

𝑉 = 𝑙𝑤ℎ

where 𝑉 is the volume, 𝑙 is the length, ℎ is the height, and 𝑤 is the width.

Therefore,

𝑉 = 9 m ∙ 5 m ∙ 12 m

𝑉 = (9 ∙ 5 ∙ 12) m3

𝑉 = 540 m3

Answer: 540 m3

2. What is the volume of a rectangular prism whose length is 4.6 cm, width is

3.8 cm, and height is 1.4 cm?


𝑉 = 𝑙𝑤ℎ


Therefore,

𝑉 = 4.6 cm ∙ 3.8 cm ∙ 1.4 cm

𝑉 = (4.6 ∙ 3.8 ∙ 1.4) cm3

𝑉 = 24.472 cm3

Answer: 24.472 cm3


3. What is the width of a rectangular prism whose volume is 216 m3 whose

length is 6 m, and height is 9 m?


𝑉 = 𝑙𝑤ℎ


Therefore,

216 m3 = (6 m ∙ 𝑤 m ∙ 9 m)

216 m3 = (6 ∙ 𝑤 ∙ 9) m3

216 = 54𝑤

𝑤 = 4

Answer: 4 m

4. What is the height of a rectangular prism whose volume is 672 cm3 whose

length is 12 cm, and width is 7 cm?


𝑉 = 𝑙𝑤ℎ


Therefore,

672 cm3 = (12 cm ∙ 7 cm ∙ ℎ cm)

672 cm3 = (12 ∙ 7 ∙ ℎ) cm3

672 = 84ℎ

ℎ = 8

Answer: 8 cm




𝑉 = 𝑙𝑤ℎ


Therefore,

𝑉 = (7 m ∙ 6 m ∙ 8 m)

𝑉 = (7 ∙ 6 ∙ 8) m3

𝑉 = 336 m3

Answer: 336 m3

6. What is the volume of this cubic prism?

The formula for calculating the volume of a cubic prism is


𝑉 = 𝑙3

where 𝑉 is the volume, 𝑙 is the length of the sides. Therefore,

𝑉 = (9 cm)3

𝑉 = (93) cm3

𝑉 = 729 cm3

Answer: 729 cm3

7. What is the volume of this rectangular prism if 𝑈𝑉 = 9 mm, 𝑆𝑌 =

15 mm, and 𝑇𝑊 = 6 mm?


𝑉 = 𝑙𝑤ℎ

where 𝑉 is the volume, 𝑙 is the length, ℎ is the height, and 𝑤 is the width. The

question gives the length, width, and height. Therefore,

𝑉 = (15 mm ∙ 9 mm ∙ 6 mm)

𝑉 = (15 ∙ 9 ∙ 6) mm3

𝑉 = 810 mm3

Answer: 810 mm3



Calculate the volume of a triangular prism by calculating the area of the base and

multiplying that area by the length of the prism.

The formula for area of the base is the area of a triangle. The formula is 𝐵 =1

2𝑏ℎ

where 𝐵 is the area of the base, 𝑏 is the length of the base of the triangle, and ℎ is

the height of the triangle. Therefore,

𝐵 =1

2∙ 24 mm ∙ 5 mm

𝐵 = (1

2∙ 24 ∙ 5) mm2

𝐵 = 60 mm2

Now multiply this area by the length of the prism to find the volume.

𝑉 = 60 mm2 ∙ 28 mm

𝑉 = (60 ∙ 28) mm2 ∙ mm

𝑉 = 1680 mm3

Answer: 1680 mm3




𝑉 = 𝑙𝑤ℎ



𝑉 = (6 km ∙ 6 km ∙ 7 km)

𝑉 = (6 ∙ 6 ∙ 7) km3

𝑉 = 252 km3

Answer: 252 km3




𝑉 = 𝑙𝑤ℎ


Therefore,

𝑉 = (3.8 cm ∙ 3.6 cm ∙ 4.1 cm)

𝑉 = (3.8 ∙ 3.6 ∙ 4.1) cm3

𝑉 = 56.088 cm3

Answer: 𝑉 = 56.088 cm3

11. What is the volume of this rectangular prism if 𝐴𝐵 = 7 cm, 𝐵𝐶 =

11 cm, and 𝐶𝐺 = 14 cm?


𝑉 = 𝑙𝑤ℎ



𝑉 = (11 cm ∙ 7 cm ∙ 14 cm)

𝑉 = (11 ∙ 7 ∙ 14) cm3

𝑉 = 1078 cm3

Answer: 1078 cm3





The formula for area of the bases is the area of a triangle. The formula is 𝐵 =1

2𝑏ℎ

where 𝐵 is the area of the base, 𝑏 is the length of the base of the triangle, and ℎ is

the height of the triangle. The base is a right triangle, so the legs are the base and

the height. Therefore,

𝐵 = (1

2∙ 6 m ∙ 6 m)

𝐵 = (1

2∙ 6 ∙ 8) m2

𝐵 = 24 m2

Now multiply the area of the base by the length of the prism to find the volume.

𝑉 = 24 m2 ∙ 16 m

𝑉 = (24 ∙ 16) m2 ∙ m

𝑉 = 384 m3

Answer: 384 m3


13. What is the volume of this heptagonal prism if the area of the base is

140 mm2?

Calculate the volume of a heptagonal prism by multiplying the area of the base by

the height of the prism.

The area of the bases is given as 140 mm2.


𝑉 = 140 mm2 ∙ 8 mm

𝑉 = (140 ∙ 8) mm2 ∙ mm

𝐴 = 1120 mm3

Answer: 1120 mm3





The formula for area of the base is the area of a triangle. That formula is 𝐵 =1

2𝑏ℎ

where 𝐵 is the area of the triangle, 𝑏 is the length of the base of the triangle, and

ℎ is the height of the triangle. The triangle at the base is an equilateral triangle,

whose height is calculated as 1

2(6)(√3) = 3√3. Therefore,

𝐵 = (1

2∙ 6 dm ∙ 3√3 dm)

𝐵 = (1

2∙ 6 ∙ 3√3) dm2

𝐵 = 9√3 dm2


𝑉 = 9√3 dm2 ∙ 13 dm

𝑉 = (9√3 ∙ 13)dm2 ∙ dm

𝑉 = 117√3 dm3

Answer: 117√3 dm3


15. What is the volume of this regular pentagonal prism if the area of the base is

30 hm2?

Calculate the volume of a regular pentagonal prism by multiplying the area of the

base by the height or length of the prism.

The area of the base is given as 30 hm2. Multiply this area by the length of the

prism.

𝑉 = 30 hm2 ∙ 15 hm

𝑉 = (30 ∙ 15) hm2 ∙ hm

𝑉 = 450 hm3

Answer: 450 hm3

16. What is the volume of a square pyramid measuring 13 m along each edge of

the base with a height of 12 m?

The formula for calculating the volume of a pyramid is 𝑉 =1

3𝐵ℎ where 𝑉 is the

volume, 𝐵 is the area of the base, and ℎ is the height of the pyramid. As such, the

value for 𝐵 is calculated using the area formula for the base of the pyramid.

In this pyramid, the base is a square, so 𝐵 = 𝑠2 = (13 m)2 = 169 m2.

Therefore, the volume is


𝑉 =1

3(169 m2 ∙ 12 m) =

1

3(169 ∙ 12) m2 ∙ m = 676 m3

Answer: 676 m3

17. What is the volume of a triangular pyramid that is 8 cm tall with a right

triangle for a base with sides 18 cm, 24 cm, and 30 cm?





In this pyramid, the base is a right triangle with legs 18 cm and 24 cm, so

𝐵 =1

2𝑏ℎ =

1

2∙ 18 cm ∙ 24 cm = 216 cm2.


𝑉 =1

3(216 cm2 ∙ 8 cm) =

1

3(216 ∙ 8) cm2 ∙ cm = 576 cm3

Answer: 576 cm3







In this pyramid, the base is a right triangle with legs 3 m and 4 m, so 𝐵 =1

2𝑏ℎ =

1

2∙ 3 m ∙ 4 m = 6 m2.


𝑉 =1

3(6 m2 ∙ 4 m) =

1

3(6 ∙ 4) m2 ∙ m = 8 m3

Answer: 8 m3






In this pyramid, the base is a rectangle with sides 11 cm and 10 cm, so

𝐵 = 𝑏ℎ = 11 cm ∙ 10 cm = 110 cm2.


𝑉 =1

3(110 cm2 ∙ 12 cm) =

1

3(110 ∙ 12) cm2 ∙ cm = 440 cm3

Answer: 440 cm3







In this pyramid, the base is a rectangle with sides 3 m and 12 m, so 𝐵 = 𝑏ℎ =

3 m ∙ 12 m = 36 m2.


𝑉 =1

3(36 m2 ∙ 13 m) =

1

3(36 ∙ 13) m2 ∙ m = 156 m3

Answer: 156 m3


pyramid is 249 cm2?






In this pyramid, the area of the pentagonal base is provided as 𝐵 = 249 cm2.


𝑉 =1

3(249 cm2 ∙ 11 cm) =

1

3(249 ∙ 11) cm2 ∙ cm = 913 cm3

Answer: 913 cm3

22. What is the volume of this pyramid if the area of the hexagonal base of the

pyramid is 93.6 m2?





In this pyramid, the area of the hexagonal base is provided as 𝐵 = 93.6 m2.


𝑉 =1

3(93.6 m2 ∙ 9 m) =

1

3(93.6 ∙ 9) m2 ∙ m = 280.8 m3

Answer: 280.8 m3







In this pyramid, the base is a right triangle with legs 6 mm and 8 mm, so

𝐵 =1

2𝑏ℎ =

1

2∙ 6 mm ∙ 8 mm = 24 mm2.


𝑉 =1

3(24 mm2 ∙ 12 mm) =

1

3(24 ∙ 12) mm2 ∙ mm = 96 mm3

Answer: 96 mm3


pyramid is 139.5 dm2?






In this pyramid, the area of the pentagonal base is provided as 𝐵 = 139.5 dm2.


𝑉 =1

3(139.5 dm2 ∙ 7 dm) =

1

3(139.5 ∙ 7) dm2 ∙ dm = 325.5 dm3

Answer: 325.5 dm3






In this pyramid, the base is a rectangle with sides 8 in and 10 in, so 𝐵 = 𝑏ℎ =

8 in ∙ 10 in = 80 in2.


𝑉 =1

3(80 in2 ∙ 15 in) =

1

3(80 ∙ 15) in2 ∙ in = 400 in3

Answer: 400 in3


26. The volume of a square pyramid is 864 m3. The height of the pyramid is 18 m.

What is the length of the edges of the base?





In this pyramid, the base is a square, so 𝐵 = 𝑠2. Use the volume formula to find

the length of the edges of the base.

Therefore,

864 m3 =1

3(𝑠2 m2 ∙ 18 m)

864 m3 =1

3(𝑠2 ∙ 18 ) m3

864 = 6𝑠2

144 = 𝑠2

𝑠 = 12

Answer: 12 m

27. The volume of a rectangular pyramid is 1080 cm3. What is the height of the

pyramid if the lengths of the edges of the base are 12 cm and 18 cm?





In this pyramid, the base is a rectangle with sides 12 cm and 18 cm, so

𝐵 = 𝑏ℎ = 12 cm ∙ 18 cm = 216 cm2.

Use the volume formula to find ℎ.

1080 cm3 =1

3(216 cm2 ∙ ℎ cm)


1080 cm3 =1

3(216 ∙ ℎ) cm3

1080 = 72ℎ

ℎ = 15

Answer: 15 cm

28. The volume of a square pyramid is 2048 mm3. What is the height of the

pyramid if the length of the edges of the base are 16 mm?





In this pyramid, the base is a square, so 𝐵 = 𝑠2 = 162 = 256 mm2. Use the

volume formula to find the length of the height.

Therefore,

2048 mm3 =1

3(256 mm2 ∙ ℎ mm)

2048 mm3 =1

3(256 ∙ ℎ ) mm3

6144 = 256ℎ

24 = ℎ

Answer: 24 mm

Geometry Tutor Worksheet 17 Volume of Prisms …...What is the volume of this regular pentagonal...

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Transcript of Geometry Tutor Worksheet 17 Volume of Prisms …...What is the volume of this regular pentagonal...