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?

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 The volume of the small box =

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 The volume of the larger base box =

Since both boxes have the same volume, therefore:

=

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

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .