Finding the Volume of Rectangular Prisms

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NEO Thu, Jan 27, 2022 01:35 PM UTC

This pdf contains the problem of rectangular prisms with step-by-step solutions. A rectangular prism can be defined as a 3-dimensional solid shape that has six faces that are rectangles.

1. ® Name:
Date:
Finding the Volume of Rectangular Prisms VOL 1
Instructions: Find the volume of each rectangular prism by multiplying the area of the ‘base’
times the length the base has been extended. (Don’t forget about the units!)
1 2
10 in 2 in
5m
8m
7 in
6m
Area = 5 × 6 = 30 m2 Area = 2 × 7 = 14 in2
of Base
of Base
Volume = 30 m2 × 8 m = 240 m3 Volume = 14 in2 × 10 in = 140 in3
3 4
5 cm
20 cm 9 ft
12 ft
5 cm
4 ft
Area = 5 × 5 = 25 cm2 Area = 9 × 4 = 36 ft2
of Base
of Base
Volume = 25 cm2 × 20 cm = 500 cm3 Volume = 36 ft2 × 12 ft = 432 ft3
5 6
3 in 4m
9 in
6m
5 in 4m
Area = 3 × 5 = 15 in2 Area = 4 × 4 = 16 m2
of Base of Base
Volume = 15 in2 × 9 in = 135 in3 Volume = 16 m2 × 6 m = 96 m3
Volume • mathantics.com © 2016 Math Plus Motion, LLC

2. ® Name:
Date:
Finding the Volume of Triangular Prisms VOL 2
Instructions: Find the volume of each triangular prism by multiplying the area of the ‘base’ times
the length the base has been extended. (Don’t forget about the units!)
1 2
10 m
4 in
12 m 8 in
9m
4 in
90
Area = 1 (9 × 10) = = 45 m2 Area =
1
(4 × 4) =
16
= 8 in2
of Base 2 2 of Base 2 2
Volume = 45 m2 × 12 m = 540 m3 Volume = 8 in2 × 8 in = 64 in3
3 4
4 cm 8 ft
18 cm
12 ft
6 cm
5 ft
1 24 40
Area = (6 × 4) = = 12 cm2 1
of Base 2 2 Area = (5 × 8) = = 20 ft2
of Base 2 2
Volume = 12 cm2 × 18 cm = 216 cm3 Volume = 20 ft2 × 12 ft = 240 ft3
5 6
7m 10 in
9m 14 in
4m 9 in
1 28 1 90
Area = (4 × 7) = = 14 m2 Area = (9 × 10) = = 45 in2
of Base 2 2 of Base 2 2
Volume = 14 m2 × 9 m = 126 m3 Volume = 45 in2 × 14 in = 630 in3
Volume • mathantics.com © 2016 Math Plus Motion, LLC

3. ® Name:
Date:
Finding the Volume of Cylinders VOL 3
Instructions: Find the volume of each cylinder by multiplying the area of the ‘base’ times the
length the base has been extended. (Use 3.14 for Pi and don’t forget about the units!)
1 2
3m
6m
20 in 5 in
Area = π × (3 m)2 = 3.14 × 9 m2 Area = π × (5 in)2 = 3.14 × 25 in2
of Base of Base
= 28.26 m2 = 78.5 in2
V = 28.26 m2 × 6 m = 169.56 m3 V = 78.5 in2 × 20 in = 1,570 in3
6m
3 4
7m
25 cm 4 cm
Area = π × (4 cm)2 = 3.14 × 16 cm2 Area = π × (6 m)2 = 3.14 × 36 m2
of Base of Base
= 50.24 cm2 = 113.04 m2
V = 50.24 cm2 × 25 cm = 1,256 cm3 V = 113.04 m2 × 7 m = 791.28 m3
1 in
5 6
2 cm
8 in
10 cm
Area = π × (1 in)2 = 3.14 × 1 in2 Area = π × (2 cm)2 = 3.14 × 4 cm2
of Base of Base
= 3.14 in2 = 12.56 cm2
V = 3.14 in2 × 8 in = 25.12 in3 V = 12.56 cm2 × 10 cm = 125.6 cm3
Volume • mathantics.com © 2016 Math Plus Motion, LLC

4. ® Name:
Date:
Finding the Volume of Spheres and Cones - Set 1 G-VOL 4
Instructions: Find the volume of each sphere or cone using the formulas given. (Use 3.14 for Pi,
round answers to two decimal places, and don’t forget about the units!)
1
Formula for a Sphere
4 2m
Volume = × π × r3
3
Formula for a Cone 4
V= × 3.14 × (2 × 2 × 2) m3
1 3
Volume = × h × π × r2
3 4 × 25.12 m3
= = 33.49 m3
3
2 3 9m
3 cm
7m
4
V= × 3.14 × (3 × 3 × 3) cm3 1
3 V= × 9 m × 3.14 × (7 × 7) m2
3
4 × 84.78 cm3
= = 113.04 cm3 = 3 m x 153.86 m2 = 461.58 m3
3
4 5
6 in
4 km
2 in
1 4
V= × 6 in × 3.14 × (2 × 2) in2 V= × 3.14 × (4 × 4 × 4) km3
3 3
= 2 in × 12.56 in2 = 25.12 in3 4 × 200.96 km3
= = 267.95 km3
3
Volume • mathantics.com © 2016 Math Plus Motion, LLC

5. ® Name:
Date:
Finding the Volume of Spheres and Cones - Set 2 G-VOL 5
Instructions: Find the volume of each sphere or cone using the formulas given. (Use 3.14 for Pi,
round answers to two decimal places, and don’t forget about the units!)
1 8m
Formula for a Sphere
4
Volume = × π × r3
3 3m
Formula for a Cone
1
V= × 8 m × 3.14 × (3 × 3) m2
1 3
Volume = × h × π × r2
3 = 2.67 m × 28.26 m2 = 75.45 m3
2 3 in 3
8 cm
2 in
1 4
V= × 3 in × 3.14 × (2 × 2) in2 V= × 3.14 × (8 × 8 × 8) cm3
3 3
= 1 in × 12.56 in2 = 12.56 in3 4 × 1607.68 cm3
= = 2,143.57 cm3
3
4 5
9 in
1.5 m
2.5 in
4
V= × 3.14 × (1.5 × 1.5 × 1.5) m3 1
3 V= × 9 in × 3.14 × (2.5 × 2.5) in2
3
4 × 10.598 m3
= = 14.13 m3 = 3 in x 19.625 in2 = 58.88 in3
3
Volume • mathantics.com © 2016 Math Plus Motion, LLC

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