Question

the lateral surface area and total surface area of a cuboid are 238cm2 and 382cm2.if the height of the cuboid is 7cm,find the volume of cuboid​

Answer 1

Answer:

504 cm³

Step-by-step explanation:

Given

The lateral surface area of the cuboid = 238 cm²

The total surface area of the cuboid = 382 cm²

The height of the cuboid = 7 cm

Let the length be 'l' and breadth be 'b'

We know that

The lateral surface area of the cuboid = 2h(l + b) sq.units

⇒2h(l + b) = 238 cm²

⇒2*7(l + b) = 238

⇒l + b = 238/14

∴ l + b = 17

⇒ b = 17 - l      _______(1)

The total surface area of the cuboid = 2(lb + bh + lh) sq.units

⇒2(lb + bh + lh) = 382 cm²

⇒lb + h(l + b) = 382/2

⇒lb + 7*(17) = 191      [∴l + b = 17]

⇒lb + 119 = 191

⇒lb = 191 - 119

⇒lb = 72

⇒l(17 - l) = 72    [from (1)]

⇒17l - l² = 72

⇒l² - 17l + 72 = 0

⇒l² - 8l - 9l + 72 = 0     [By factorization method]

⇒l(l - 8) - 9(l - 8) = 0

⇒(l - 9)*(l - 8) = 0

⇒l = 9cm or l = 8 cm

From (1)

⇒ b = 17 - l

If l = 9 cm then b = 17 - 9 = 8 cm

If l = 8 cm then b = 17 - 8 = 9 cm

So, b = 8 cm or b = 9 cm

Since it is a cuboid, length  and breadth cannot be equal. So we should take different values of length and breadth.

If l = 8 cm then b = 9 cm

If l = 9 cm then b = 8 cm

Let us take l = 8 cm and b = 9 cm

∴The volume of the cuboid = l*b*h cubic.units

                                               = 8*9*7 cm³

∴The volume of the cuboid = 504 cm³

The same result will come if we take l = 9 cm and b = 8 cm

∴The volume of the cuboid = 504 cm³