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
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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
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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