Question

if the volume of a cuboid is 540cm³ and its Lateral surface area is 154cm³. Find its height. correct answers will be marked brainliest.​

Answer 1

The height of a cuboid given volume of a cuboid to be $540cm^3$ and its lateral surface area to be $154cm^3$ is $h=\dfrac{77}{l+b}$ with l and b being length and breadth.

• Given,
• The volume of a cuboid
• $=540cm^3\\\\lbh=540\\\\h=\dfrac {540}{lb}$......(1)
• The lateral surface area of a cuboid
• $=154 cm^3\\\\2h(l+b)=154\\\\h=\dfrac{154}{2(l+b)}$......(2)
• from (1) we have,
• $\dfrac{540}{lb}=\dfrac{154}{2(l+b)}\\\\lb=\dfrac{1080(l+b)}{154}$...........(3)
• again susbtituting the equation (3) in (1), we get,
• $h=\dfrac{540}{\frac{1080(l+b)}{154}}\\\\\\h=\dfrac{77}{l+b}$

Answer 2

The height of the cuboid is $\frac{77}{l+b}$

Step-by-step explanation:

Given Data

Volume of the cuboid = 540 cm³

Lateral surface area of the cuboid = 154 cm³

To find the height of the cuboid

Volume is generally defines as the ratio between mass and density.

The formula for volume of cuboid = length × breadth × height

Volume of cuboid = l × b × h

540  cm ³ = lbh

Also the above equation can be written as,

$h = \frac{540}{lb}$     ------> (1)

Lateral surface area of the cuboid = 2 h (l + b)

154 = 2 h (l + b)

$h = \frac{154}{2( l + b )}$  ------> (2)

Equate (1) and (2)

$\frac{154}{2( l + b )} = \frac{540}{lb}$

$lb = \frac{540}{\frac{154}{2(l+ b)} }$  

$lb = \frac{540 \times 2 \times (l + b)}{154}$

$lb = \frac{1080 \times (l + b)}{154}$   --------> (3)

Substitute the value of lb in equation (1)

$h = \frac{540 \times 154}{ 1080 \times ( l+ b) }$

$h = \frac{77}{ ( l + b )}$

Therefore the height of the cuboid of volume 540 cm³ and lateral surface area 154 cm² is $\frac{77}{ l + b )}$

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