Answer:
Logically, the answer is the sphere, as it is the figure which gives maximum volume for the same total surface area. But I'll just solve them like you want it.
I'm just writing the numerical values without the units.Please resolve
Solid 1: Square Prism with each side of the base equal to 8 in. and a height of 8 in.
Volume = 8^3 = 512
Area = 8^2 * 6 = 384
V/A Ratio = 1.33 (We need the highest ratio, that's why they hired us)
Cost = $7.68
Solid 2: Square Pyramid with each side of the base equal to 10 in. and a height of 15 in.
Volume = 1/3 * 10^2 * 15 = 500
Slant height = [(10/2)^2 + 15^2]^(1/2) = root of 250 = 15.81
Area = 2*10*15.81 + 10^2 = 416.23
V/A Ratio = 1.20
Cost = $8.34
Solid 3: Cylinder with a radius of 4 in. and a height of 10 in.
Volume = pi*4*4*10 = 502.65
Area = 2*pi*4*4 + 2*pi*4*10 = 351.86
V/A Ratio = 1.43
Cost = $7.04
Solid 4: Cone with a radius of 7 in. and a height of 10 in.
Volume = (1/3)*pi*7*7*10 = 513.13
Slant height = [(7^2)+(10^2)]^(1/2) = 12.21
Area = pi*7*12.21 + pi*7*7 = 422.37
V/A Ratio = 1.21
Cost = $8.45
Solid 5: Sphere with a radius of 5 in.
Volume = (4/3)*pi*(5^3) = 523.60
Area = 4*pi*(r^2) = 314.16
V/A Ratio = 1.67
Cost = $6.28
Hence, Solid 5 must be the packaging model opted for
Step-by-step explanation:
Logically, the answer is the sphere, as it is the figure which gives maximum volume for the same total surface area. But I'll just solve them like you want it.
I'm just writing the numerical values without the units.Please resolve
Solid 1: Square Prism with each side of the base equal to 8 in. and a height of 8 in.
Volume = 8^3 = 512
Area = 8^2 * 6 = 384
V/A Ratio = 1.33 (We need the highest ratio, that's why they hired us)
Cost = $7.68
Solid 2: Square Pyramid with each side of the base equal to 10 in. and a height of 15 in.
Volume = 1/3 * 10^2 * 15 = 500
Slant height = [(10/2)^2 + 15^2]^(1/2) = root of 250 = 15.81
Area = 2*10*15.81 + 10^2 = 416.23
V/A Ratio = 1.20
Cost = $8.34
Solid 3: Cylinder with a radius of 4 in. and a height of 10 in.
Volume = pi*4*4*10 = 502.65
Area = 2*pi*4*4 + 2*pi*4*10 = 351.86
V/A Ratio = 1.43
Cost = $7.04
Solid 4: Cone with a radius of 7 in. and a height of 10 in.
Volume = (1/3)*pi*7*7*10 = 513.13
Slant height = [(7^2)+(10^2)]^(1/2) = 12.21
Area = pi*7*12.21 + pi*7*7 = 422.37
V/A Ratio = 1.21
Cost = $8.45
Solid 5: Sphere with a radius of 5 in.
Volume = (4/3)*pi*(5^3) = 523.60
Area = 4*pi*(r^2) = 314.16
V/A Ratio = 1.67
Cost = $6.28
Hence, Solid 5 must be the packaging model opted for
