Question

The area of a base of a cuboid is 30 cm^2 and it's volume is 135 cm^3.Find the height of the cuboid​

Answer 1

Answer:

4.5 cm

Step-by-step explanation:

As per the provided information in the given question, we have:

• The area of the base of a cuboid is 30 cm².
• Volume of the cuboid is 135 cm³.

We've been asked to calculate the height of the cuboid.

Area of the base of the cuboid is in the shape of rectangle. So,

$\twoheadrightarrow\quad\sf{{Area}_{(Rectangle)}=l\times b}$

Here, we are given that the area of the rectangle is 30 cm². Substitute the area.$\\\twoheadrightarrow\quad\sf{30=l\times b\qquad\quad\qquad\qquad\left\lgroup\begin{matrix}\sf{{eq}^{n}(1)}\end{matrix}\right\rgroup}$

– Now, according to the question, the volume of the cuboid is 135 cm³. We know, volume of cuboid is product of length, breadth and height. So,

$\twoheadrightarrow\quad\sf{{Volume}_{(Cuboid)}=l\times b\times h}$

Equating volume of cuboid.

$\twoheadrightarrow\quad\sf{135=l\times b\times h}$

From eqⁿ (1),

$\twoheadrightarrow\quad\sf{135=30\times h}$

Transposing 30 from RHS to LHS. It's arithmetic operator will get change.

$\twoheadrightarrow\quad\sf{\dfrac{135}{30}=h}$

Performing division.

$\twoheadrightarrow\quad\underline{\boxed{\pmb{\frak{h=4.5\; cm}}}}$

❝ Therefore, height of the cuboid is 4.5 cm. ❞

Answer 2

Area =l×b=180

⇒Volume of cuboid =l×b×h=900

⇒180×h=900

⇒h=180900=5 cm