Question

two boxes have the same volume. One box has a base that is 5 cm5\text{ cm}5 cm5, start text, space, c, m, end text by 5 cm5\text{ cm}5 cm5, start text, space, c, m, end text. The other box has a base that is 10 cm10\text{ cm}10 cm10, start text, space, c, m, end text by 10 cm10\text{ cm}10 cm10, start text, space, c, m, end text. How many times as tall is the box with the smaller base?

Answer 1

Answer:

The height of the box with the smaller base is 4  times that of the box with the larger base

Step-by-step explanation:

The volume of a box is the product of the base area and the height of the box, it is given as:

Volume = base area × height

For the smaller base box, it has a base of 5 cm by 5 cm, therefore the base area of the smaller base box = 5 cm × 5 cm  = 25 cm². Let the height of the smaller base box be $h_1$The volume of the small box = $25*h_1$

For the larger base box, it has a base of 10 cm by 10 cm, therefore the base area of the larger base box = 10 cm × 10 cm  = 100 cm². Let the height of the large base box be $h_2$The volume of the larger base box = $100*h_2$

Since both boxes have the same volume, therefore:

$100*h_2$ = $25*h_1$

$\frac{h_1}{h_2} =\frac{100}{25} \\\\\frac{h_1}{h_2}=4\\\\h_1=4h_2$

The height of the box with the smaller base is 4  times that of the box with the larger base

Answer 2

We can use the formula V=lwh to compare the volume in the two boxes.

First let's compare the volume of both boxes to see if they have the same height. To make it simple, let's use a height of 1 centimeter.

First the box with the smaller base.

V=lwh

V=5⋅5⋅1

V=25

Now the box with the larger base

V=lwh

V=10x10x1

V=100

We can set up an equation to find out how many times as tall the smaller box needs to be to have the same volume as the box with the larger base.

25·h=100

h=4

The boz with the smaller base is 4 times tall

hope it helped :)

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