Question

The total surface area of this cuboid is 112cm^2. Find the value of x.

Please explain, don’t just give the answer.

Answer 1

= 3

Explanation:

(easier way to solve it)

x = L, 10 = B, 2 = W

L x B

x 10 = A1

L x W

x 2 = A2

B x W

10 x 2 = 20 (A3)

= 112cm^2 / 2 = 56cm - 20 = 36

3 x 10 = 30

3 x 2 = 6

30 + 6 = 36

36 + 20 = 56cm

56cm x 2 = 112cm^2

(i hope this actually makes sense, things work differently in my mind)

Answer 2

The value of x is 3

Explanation:

Let us study the face of the cuboind

∵ The cuboid has 6 rectangular faces

∵ Each opposite faces area equal in areas

∴ 2 faces of dimensions 10 cm and 2 cm

∴ 2 faces of dimensions 10 cm and x cm

∴ 2 faces of dimensions 2 cm and x cm

∵ The total surface area of the cuboid is the sum of the areas of the 6 faces

∵ The area of the rectangle = length × width

∴ The total surface area = 2(10 × 2) + 2(10 × x) + 2(2 × x)

∴ The total surface area = 2(20) + 2(10x) + 2(2x)

∴ The total surface area = 40 + 20x + 4x

→ Add the like terms 20x and 4x

∴ The total surface area = 40 + 24x

∵ The total surface area of this cuboid is 112 cm²

→ Equate the two sides of the total surface area

∴ 40 + 24x = 112

→ Subtract 40 from both sides

∵ 40 - 40 + 24x = 112 - 40

∴ 24x = 72

→ Divide both sides by 24

∴ x = 3

∴ The value of x is 3