Step-by-step explanation:
#1 Surface area of the rectangular box:
The formula for the surface area of a rectangular box is given by:
SA= 2lw + 2lh + 2wh, where
- SA is the surface area in square units,
- l is the length,
- w is the width,
- and h is the height.
In this rectangular box, the length is 5 cm, the width is 7 cm, and the height is 2 cm.
Thus, we can plug in 5 for l, 7 for w, and 2 for h in the rectangular box formula to find SA, the surface area of the rectangular box in square cm:
SA = 2(5 * 7) + 2(5 * 2) + 2(7 * 2)
SA= 2(35) + 2(10) + 2(14)
SA = 70 + 20 + 28
SA = 118
Thus, the surface area of the rectangular box is 118 cm^2.
#1 Volume of the rectangular box:
The formula for the volume of a rectangular box is given by:
V = lwh, where
- V is the volume in cubic units.
Thus, we can plug in 5 for l, 7 for w, and 2 for h in the rectangular box formula to find V, the volume of the rectangular box in cubic units:
V = 5 * 7 * 2
V = 70
Thus, the volume of the rectangular box is 70 cm^3.
#2 Surface area of the cube:
The formula for the surface area of a cube is given by:
SA = 6s^2, where
- SA is the surface area in square units,
- and s is the length of the edges.
Thus, we can plug in 4.5 for s in the surface area formula to find SA, the surface area of the cube in square in.:
SA = 6(4.5)^2
SA = 6(20.25)
SA = 121.5
Thus, the surface area of the cube is 121.5 in^2.
#2 Volume of the cube:
The formula for the volume of a cube is given by:
V = s^3, where
- V is the volume in cubic units.
Thus, we can plug in 4.5 for s in the volume formula to find V, the volume of the cube in square in.:
V = 4.5^3
V = 91.125
Thus, the volume of the cube is 912.125 in^3.
#3 Surface area of the triangular prism:
One formula we can use for the surface area of a triangular prism is given by:
SA = bh + L(s1 + s2 + s3), where
- b is the base of one of the triangles,
- h is the height of the triangular prism (i.e., the height of one of the triangles),
- L is the length of the prism (i.e., the distance between the two triangles),
- and s1, s2, and s3 are the three side lengths of one of the triangles.
In this triangular prism, the base is 6 in., the height is 8 in., the length is 6 in., and the three side lengths of one of the triangles are 8 in., 6 in., and 10 in.
Thus, we can plug in 6 for b, 8 for h, 6 for L, and 8, 6, and 10 for s1, s2, and s3 in the triangular prism surface area formula to find SA, the surface area of the triangular prism in square meters:
SA = 6 * 8 + 6(8 + 6 + 10)
SA = 48 + 6(24)
SA = 48 + 144
SA = 192
Thus, the surface area of the triangular prism is 192 m^2.
#3 Volume of the triangular prism:
The formula for the volume of a triangular prism is given by:
V = 1/2bhl, where
- V is the volume in cubic units.
Thus, we can plug in 6 for b, 8 for h, and 6 for l in the triangular prism volume formula to find V, the volume of the triangular prism in cubic meters:
V = 1/2(6)(8)(6)
V = 3 * 48
V = 144
Thus, the volume of the triangular prism is 144 m^3.
#4 Surface area of the triangular prism:
Because this figure is also a triangular prism, we can use the same formulas to surface area and volume as we used for #3.
- Just note that the base is the base of the entire triangle,
- and the height is the line from the top of one of the triangles to its base
Since the formula for surface area of a triangular prism is given by:
SA = bh + L(s1 + s2 + s3), we can plug in 12 for b, 8 for h, 12 for L, and 10, 10, and 12 for s1, s2, and s3 in the surface area formula to find SA, the surface area of the triangular prism in cubic ft:
SA = 12 * 8 + 12(10 + 10 + 12)
SA = 96 + 12(32)
SA = 96 + 384
SA = 480
Thus, the surface area of the triangular prism is 480 ft^2.
#4 Volume of the triangular prism:
Since the volume for the volume of a triangular prism is given by:
V = 1/2bhl, we can plug in 12 for b, 8 for h, and 12 for l in the triangular prism volume formula to find V, the volume of the triangular prism in cubic ft:
V = 1/2(12)(8)(12)
V = 6 * 96
V = 576
Thus, the volume of the triangular prism is 576 ft^3.
#5 Surface area of the cylinder:
The formula for the surface area of a cylinder is given by:
SA = 2πrh + 2πr^2, where
- SA is the surface in square units,
- r is the radius of one of the circles,
- and h is the height of the cylinder.
In the cylinder, the radius of one of the circles is 2 yd and the height of the cylinder is 5 yd.
Thus, we can plug in 2 for r and 5 for h to find SA, the surface area of the cylinder in square yd:
SA = 2π(2)(5) + 2π(2)^2
SA = 2π(10) + 2π(4)
SA = 20π + 8π
SA = 28π
SA = 87.9645943
SA = 87.96
Thus, the surface area of the cylinder is about 87.96 yd^2.
#5 Volume of the cylinder:
The formula for the volume of a cylinder is given by:
V = πr^2h, where
- V is the volume in cubic units.
Thus, we can plug in 2 for r and 5 for h in the cylinder volume formula to find V, the volume of the cylinder in cubic yd:
V = π(2)^2 * 5
V = 4π * 5
V = 20π
V = 62.83185307
V = 62.83
Thus, the volume of the cylinder is about 62.83 yd^3.