Question

10. A cuboid has total surface area 4048 cm² and lateral surface area is 253 cm. Find the area of its
base​

Answer 1

Answer:

• Area of its base = 1897.50 cm²

Step-by-step explanation:

Given that:

• A cuboid has total surface area 4048 cm².
• Lateral surface area is 253 cm².

To Find:

• Area of its base.

Formula used:

• T.S.A = 2(LB + BH + HL)
• C.S.A = 2H(L + B)
• A = (L × B)

Here,

• T.S.A = Total surface area of cuboid
• C.S.A = Lateral surface area of cuboid
• A = Area of base
• L = Length of cuboid
• B = Breadth of cuboid
• H = Height of cuboid

Finding the area of base:

We know: C.S.A + 2A = T.S.A

• Substituting the values.

→ 253 + 2A = 4048

→ 2A = 4048 - 253

→ 2A = 3795

→ A = 3795/2

→ A = 1897.50

∴ Area of base = 1897.50 cm²

Answer 2

Given

• Total surface area of cuboid = 4048 cm²
• Lateral surface area of cuboid = 253 cm²

To find

• Area of its base

Solution

We know that curved or lateral surface area means area of 4 faces and total surface area means area of 6 faces, and we have both of these values, so now we shall find area of its base, that means area of 2 faces.

So, the required solution will be :-

• C.S.A + Area of its base = T.S.A
• Area of its base = 4048 - 253
• Area of its base = 3795

∵ Area of its base = 2 × face

• 2 × A = 3795
• A = 3795/2
• A = 1897.50 cm²

Hence, the area of its base (cuboid) is 1897.50 cm²