Question

given that the total surface area of a cuboid with a square base is 66cm^2 and the total length of the sides is 40c. Find the possible volume of the cuboid.

Answer 1

660cm^3

Explanation:

to find the volume of a square with surface area, you multiply the base by the height. So the base is 66 and the height is 10(because 40/4=10). Then 66x10=660. So 660cm^3 would be your answer. Hope that helps!

Answer 2

36 cm³

≈ 35.85 cm³

Explanation:

Given cuboid with:

• Total surface area = 66 cm²
• Total length of the sides = 40 cm

To find:

• Volume of cuboid

Solution

Let side of the base be x and height be y

Then we have equatins for total surface area and total side length:

• 2*x² + 4*xy = 66 ⇒ x² + 2xy = 33
• 2*4x + 4y = 40 ⇒ 2x + y = 10 ⇒ y = 10 - 2x

Substituting y in the first equation:

• x² + 2x(10 - 2x) = 33
• x² + 20x - 4x² = 33
• -3x² + 20x - 33 = 0
• 3x² - 20x + 33 = 0

Solving the quadratic equation we get roots of:

• x₁ = 3 cm
• x₂ = 11/3 cm

For x = 3, the value of y:

• y₁ = 10 - 2x = 10 - 6 = 4 cm

For x = 11/3, the value of y:

• y₂ = 10 - 2x = 10 - 22/3 = 8/3 cm

Based on the found values we get 2 possible volumes:

• V = base * height = x²y
• V₁ = 3²*4 = 36 cm³
• V₂ = (11/3)²*8/3 ≈ 35.85 cm³