Galera me ajuda.
The volume of the cylinder is:
v₁ = (π.d²/4) * h → where d is the diameter of the cylinder and where h is the height of the cylinder
The volume of the cube is:
v₂ = AB * AD * AE → but you know that a cube has 3 equal sides
v₂ = AB³
The total volume is:
v = v₁ + v₂
v = [(π.d²/4) * h] + AB³ → given that: h = AE = AB
v = [(π.d²/4) * AB] + AB³
By using the Pythagorean's theorem:
AC² = AB² + BC² → because the square: BC = AB
AC² = AB² + AB²
AC² = 2.AB² → you know that: d = AC
d² = 2.AB²
Recall the total volume:
v = [(π.d²/4) * AB] + AB³ → we've just seen that: d² = 2.AB²
v = [(π * 2.AB²/4) * AB] + AB³
v = (π * 2.AB³/4) + AB³
v = (π * AB³/2) + AB³
v = AB³.[(π/2) + 1]
v = AB³.(π + 2)/2 → given that the volume is: 32.(π + 2)
AB³.(π + 2)/2 = 32.(π + 2)
AB³.(π + 2) = 64.(π + 2)
AB³ = 64
AB³ = 4³
AB = 4 → recall AB is the height of the cylinder and AB is the height of the cube too
Recall:
d = AB.√2 → we've just seen that: AB = 4
d = 4√2
Lateral surface area of the cylinder:
a = π.d * h → where: h is the height of the cylinder, similar to the edge of the cube, i.e. AB
a = π.d * AB → we know that: AB = 4
a = 4π.d → we know that: d = 4√2
a = 4π * 4√2
a = 16π√2
a ≈ 71.086
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Answers & Comments
The volume of the cylinder is:
v₁ = (π.d²/4) * h → where d is the diameter of the cylinder and where h is the height of the cylinder
The volume of the cube is:
v₂ = AB * AD * AE → but you know that a cube has 3 equal sides
v₂ = AB³
The total volume is:
v = v₁ + v₂
v = [(π.d²/4) * h] + AB³ → given that: h = AE = AB
v = [(π.d²/4) * AB] + AB³
By using the Pythagorean's theorem:
AC² = AB² + BC² → because the square: BC = AB
AC² = AB² + AB²
AC² = 2.AB² → you know that: d = AC
d² = 2.AB²
Recall the total volume:
v = [(π.d²/4) * AB] + AB³ → we've just seen that: d² = 2.AB²
v = [(π * 2.AB²/4) * AB] + AB³
v = (π * 2.AB³/4) + AB³
v = (π * AB³/2) + AB³
v = AB³.[(π/2) + 1]
v = AB³.(π + 2)/2 → given that the volume is: 32.(π + 2)
AB³.(π + 2)/2 = 32.(π + 2)
AB³.(π + 2) = 64.(π + 2)
AB³ = 64
AB³ = 4³
AB = 4 → recall AB is the height of the cylinder and AB is the height of the cube too
Recall:
d² = 2.AB²
d = AB.√2 → we've just seen that: AB = 4
d = 4√2
Lateral surface area of the cylinder:
a = π.d * h → where: h is the height of the cylinder, similar to the edge of the cube, i.e. AB
a = π.d * AB → we know that: AB = 4
a = 4π.d → we know that: d = 4√2
a = 4π * 4√2
a = 16π√2
a ≈ 71.086