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

4times tall

Step-by-step explanation:

Volume of the boxes = Base area × height

Volume of the first box V1 = A1h1

Given the base of the first box to be 5cm, the base area:

A1 = 5cm×5cm = 25cm²

Volume of the first box V1 = 25h1... 1

Similarly, volume of the second box

V2 = A2h2

Given the base of the second box to be 10cm, the base area:

A2= 10cm×10cm = 100cm²

Volume of the second box

V2 = 100h2... 2

If the two boxes have the same volume, then V1 = V2

25h1 = 100h2

divide both sides by 25

25h1/25 = 100h2/25

h1 = 4h2

Since the height of the smaller box is represented as h1, then the height of the smaller base is 4 times tall.

answer: the answer is ann