Answer:
a) S_tot 320 cm² (cube), 282.743339 cm² (cylinder) thus the cube is a greater surface area.
b) V = 300 cm³ (cube) V = 314.159265 cm³ (cylinder) thus the cylinder has a greater volume.
Step-by-step explanation:
First solve for the cube:
length l = 10 cm
width w = 10 cm
height h = 3 cm
diagonal d = 14.4568323 cm
total surface area Stot = 320 cm²
lateral surface area S_lat = 120 cm²
top surface area S_top = 100 cm²
bottom surface area S_bot = 100 cm²
volume V = 300 cm³
Agenda: l = length
w = width
h = height
d = diagonal
S_tot = total surface area
S_lat = lateral surface area
S_top = top surface area
S_bot = bottom surface area
V = volume
Formulas for a rectangular prism or cube:
Volume of Rectangular Prism:
V = lwh
Surface Area of Rectangular Prism:
S = 2(lw + lh + wh)
Space Diagonal of Rectangular Prism:
d = √(l² + w² + h²)
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Second we solve for the cylinder
radius r = 5 cm d/2 = 10/2 = 5 cm
height h = 4 cm
volume V = 314.159265 cm³
lateral surface area L = 125.663706 cm²
top surface area T = 78.5398163 cm²
base surface area B = 78.5398163 cm²
total surface area A = 282.743339 cm²
In Terms of Pi π
volume V = 100 π cm³
lateral surface area L = 40 π cm²
top surface area T = 25 π cm²
base surface area B = 25 π cm²
total surface area A = 90 π cm³
Agenda:
Agenda: l = length
w = width
h = height
d = diagonal
S_tot = total surface area
S_lat = lateral surface area
S_top = top surface area
S_bot = bottom surface area
V = volume
Cylinder Formulas in terms of r and h:
Calculate volume of a cylinder:
V = πr²h
Calculate the lateral surface area of a cylinder (just the curved outside):
L = 2πrh
Calculate the top and bottom surface area of a cylinder:
T = B = πr²
Total surface area of a closed cylinder is:
A = L + T + B = 2πrh + 2(πr²) = 2πr(h+r)
