Question

A cuboid has total surface area 280 cm^2. If its breadth is 5 cm and height is 6 cm, find its length. Also find the perimeter of its base.

Answer 1

Question :-

A cuboid has total surface area 280 cm². If its breadth is 5 cm and height is 6 cm, find its length. Also find the perimeter of its base.

To find :-

• length of the cuboid.
• perimeter of base of the cuboid.

We have :-

• surface area of cuboid = 280 cm²
• breadth of cuboid = 5 cm
• height of cuboid = 6 cm

Formula used :-

surface area of cuboid = 2(lb + bh + lh)

perimeter of base of cuboid = 2(l + b)

Solution :-

surface area of cuboid = 2(lb + bh + lh)

put the values of surface area, breadth, and height of the cuboid .

we get,

280 = 2(L×5 + 5×6 + L×6)

280 = 2( 5L + 30 + 6L)

280 = 2(11L + 30)

280 = 22L + 60

280 - 60 = 22L

220 = 22L

L = 220/22

L = 10 cm

∴ the length of the cuboid = 10 cm

Now we have to find out the perimeter of the base of cuboid .

perimeter of base = 2(l + b)

= 2(10 + 5)

= (2 × 15) cm

= 30 cm

therefore the length of the cuboid is 10 cm and perimeter of the base is 30 cm

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