Two boxes have the same volume. One box has a base that is 5cm by 5cm. The other box has a base that is 10cm by 10cm. How many times as tall is the box with the smaller base? times as tall

Set Up Equation: Let's denote the height of the box with the smaller base as $ h_1 $ and the height of the box with the larger base as $ h_2 $. Since the volumes of the two boxes are the same, we can set up the equation for volume for both boxes and equate them. Volume of a box = base area × height. For the smaller base box: $ 5 \text{cm} \times 5 \text{cm} \times h_1 $. For the larger base box: $ 10 \text{cm} \times 10 \text{cm} \times h_2 $. Equating the volumes: $ 5 \times 5 \times h_1 = 10 \times 10 \times h_2 $.Simplify Equation: Now we simplify the equation: $ 25h_1 = 100h_2 $. To find out how many times as tall the box with the smaller base is, we need to solve for $ h_1/h_2 $. $ h_1/h_2 = 100/25 $.Find Ratio: Simplify the fraction $ 100/25 $ to find the ratio of $ h_1 $ to $ h_2 $: $ h_1/h_2 = 4/1 $. This means that the box with the smaller base is 4 times as tall as the box with the larger base.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Two boxes have the same volume. One box has a base that is
5cm by
5cm. The other box has a base that is
10cm by
10cm.
How many times as tall is the box with the smaller base?
times as tall

Two boxes have the same volume. One box has a base that is $5 \mathrm{~cm}$ by $5 \mathrm{~cm}$ . The other box has a base that is $10 \mathrm{~cm}$ by $10 \mathrm{~cm}$ . $\newline$ How many times as tall is the box with the smaller base? $\newline$ $\square$ times as tall

View step-by-step help

Full solution

Q. Two boxes have the same volume. One box has a base that is

5 \mathrm{~cm}

5 \mathrm{~cm}

. The other box has a base that is

10 \mathrm{~cm}

10 \mathrm{~cm}

\newline

How many times as tall is the box with the smaller base?

\newline

\square

times as tall

Set Up Equation: Let's denote the height of the box with the smaller base as $h_1$ and the height of the box with the larger base as $h_2$ . Since the volumes of the two boxes are the same, we can set up the equation for volume for both boxes and equate them. $\newline$ Volume of a box = base area × height. $\newline$ For the smaller base box: $5 \text{cm} \times 5 \text{cm} \times h_1$ . $\newline$ For the larger base box: $10 \text{cm} \times 10 \text{cm} \times h_2$ . $\newline$ Equating the volumes: $5 \times 5 \times h_1 = 10 \times 10 \times h_2$ .
Simplify Equation: Now we simplify the equation: $\newline$ $25h_1 = 100h_2$ . $\newline$ To find out how many times as tall the box with the smaller base is, we need to solve for $h_1/h_2$ . $\newline$ $h_1/h_2 = 100/25$ .
Find Ratio: Simplify the fraction $100/25$ to find the ratio of $h_1$ to $h_2$ : $\newline$ $h_1/h_2 = 4/1$ . $\newline$ This means that the box with the smaller base is $4$ times as tall as the box with the larger base.