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Find the volume of a rectangular box with the given length, breadth, and height respectively. $2p$ ,$4q$ , $8r$
A. $4pqr$
B. $64pqr$
C. $6pr$
D. $4pq$

Last updated date: 16th Jun 2024
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Hint: The volume of the rectangular solid is given by the product of length (l), width (b), and height (h).
$\therefore $ $V = lbh$
Put $l = 2p$, $b = 4q$ and $h = 8r$ into the formula $V = lbh$.

Complete answer:
Consider a rectangular box whose length is $2p$ , breadth is $4q$ and height is $8r$.
The volume of a rectangular solid is the product of the length, breadth, and height.
$V$ =Length $ \times $ breadth $ \times $ height
Substitute Length=$2p$, breadth=$4q$ and height=$8r$ into the formula of volume.
\[V\; = 2p \times 4q \times 8r\]
\[V\; = (2 \times 4 \times 8)pqr\]
\[V\; = 64pqr\]

Final Answer: The volume of a rectangular box with the given length$2p$, breadth$4q$, and height $8r$is \[64pqr\].

The formula for finding volume should be correct. Students may get confused with the formulas of volume and the areas.
Here are some list formulas for finding volume and area.
Volume of a rectangular box,$V = lbh$
Surface area of a rectangular box, $S = 2lb + 2bh + 2lh$
Where length =(l), width= (b), and height =(h).
Area of a Square , \[A{\text{ }} = {\text{ }}{a^2}\]
Where $a$ = Length of the sides of a Square
Area of a Rectangle ,\[A{\text{ }} = {\text{ }}l \times b\]
Where, l = Length ; b = Breadth
Area of a Triangle , \[A{\text{ }} = {\text{ }}\dfrac{1}{2} \times b \times h\]
Where, \[b\] = base of the triangle; \[h\] = height of the triangle
Surface Area of a Sphere ,\[S{\text{ }} = {\text{ }}4\pi {r^2}\]
Volume of a Sphere ,\[V{\text{ }} = {\text{ }}\dfrac{4}{3} \times \pi {r^3}\]
Where, $r$ = Radius of the Sphere