Question

the width of a box is two thirds its length and height is one third of length. if the volume is 48cm³. find the area of base of the box?

Answer 1

Answer:

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Answer 2

Given :

• The width of a box is two thirds its length and height is one third of length.

• The volume of box = 48 cm³.

To find :

• The area of base of the box =?

Step-by-step explanation :

Let, the length of the box be, x.

Then, the width of the box be, x × 2/3 = 2x/3

And, the height of the box be, x × 1/3 = x/3

Now,

We know that,

Volume of the box = Volume of cuboid = length × breadth × height

According to the question :

➮ 48 = x × 2x/3 × x/3

➮ 48 = 2x³/9

➮ 2x³ = 48 × 9

➮ 2x³ = 432

➮ x³ = 432/2

➮ x³ = 216

➮ x = 6

Therefore, We got the value of, x = 6 cm.

Hence,

The length of the box, x = 6 cm.

The width of the box, 2x/3 = 2 × 6/3 = 12/3 = 4 cm.

The height of the box, x/3 = 6/3 = 2 cm.

Now,

We know that,

Length of the box = 6 cm.

Width of the box = 4 cm

So,

Area of the base of the box = Area of rectangle j length × breadth

Substituting the values in the above formula, we get,

= 6 × 4

= 24.

Therefore, Area of the base of the box = 24 cm².