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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:

lengthl = 10 cm

widthw = 10 cm

heighth = 3 cm

diagonald = 14.4568323 cm

total surface areaStot = 320 cm²

lateral surface areaS_lat = 120 cm²

top surface areaS_top = 100 cm²

bottom surface areaS_bot = 100 cm²

volumeV = 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)

Second we solve for the cylinder

radiusr = 5 cm  d/2 = 10/2 = 5 cm

heighth = 4 cm

volumeV = 314.159265 cm³

lateral surface areaL = 125.663706 cm²

top surface areaT = 78.5398163 cm²

base surface areaB = 78.5398163 cm²

total surface areaA = 282.743339 cm²

In Terms of Pi π

volumeV = 100 π cm³

lateral surface areaL = 40 π cm²

top surface areaT = 25 π cm²

base surface areaB = 25 π cm²

total surface areaA = 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)

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