The length, breadth and height of a cuboid are increased by 30%, 20% and 10% respectively, by what percent will the volume of cuboid increase?

Question: The length, breadth and height of a cuboid are increased by 30%, 20% and 10% respectively, by what percent will the volume of cuboid increase?

• 70%
• 71.6%
• 75%
• 77.6%

Answer: 

✔️Formula for Volume Change:

$$\text{Increase in Volume}=x+y+z+\frac{xy}{100}+\frac{yz}{100}+\frac{zx}{100}+\frac{xyz}{1000}$$

• $x = 30\%$

• $y = 20\%$

• $z = 10\%$

$$= 30 + 20 + 10 + \frac{30 \times 20}{100} + \frac{20 \times 10}{100} + \frac{10 \times 30}{100} + \frac{30 \times 20 \times 10}{1000}$$ $$= 60 + 6 + 2 + 3 + 0.6$$ $$=71.6\mathrm{\%}$$

Additional Information :

Let's assume the original dimensions are:

• Length = $L$

• Breadth = $B$

• Height = $H$

After the increase:

• New Length = $L \times (1 + 0.30) = 1.3L$

• New Breadth = $B \times (1 + 0.20) = 1.2B$

• New Height = $H \times (1 + 0.10) = 1.1H$

• Original Volume, $V = L \times B \times H$

• New Volume, $V' = 1.3L \times 1.2B \times 1.1H$

$$V' = 1.3 \times 1.2 \times 1.1 \times L \times B \times H$$ $$= 1.716 \times L \times B \times H$$

Percentage Increase in Volume =

$$\frac{\text{New Volume} - \text{Original Volume}}{\text{Original Volume}} \times 100$$ $$= \frac{1.716LBH - LBH}{LBH} \times 100$$ $$= (1.716 - 1) \times 100$$ $$= 0.716 \times 100$$ $$= 71.6\%$$

If you find this content helpful, consider supporting us by clicking on any of the ads on this page.

Mock Test Click Here

Madhyamik Previous Year Solution Click Here

CBSE Class 10 History Notes Click Here

You Can Translate It In Your Language: