# Measurement

## Growing Pains

On September 28th, at Ciara’s appointment for her annual physical exam, she measured 3 feet 11.5 inches tall. At her last appointment on May 31st, she measured 4 feet 3 inches. Based on this, what was the average number of inches Ciara grew each day from September 28th to May 31st? Express your answer as a common fraction.

## Thirst Quencher

In the summer months, a common problem people suffer from is dehydration – not enough water in their body. Waiting until you feel thirsty is not a good indicator that it’s time to drink water. In fact, once thirst has settled in, you are already dehydrated! A general guideline is that people should drink eight 8-ounce glasses of water per day. According to this guideline, how many gallons of water should a person drink in a day, given that 1 gallon = 4 quarts and 1 quart = 32 ounces? Express your answer as a decimal to the nearest tenth.

## Fly a Kite

Molly has sketched a design for her new kite on a coordinate grid. The sides of her quadrilateral kite design are given by the equations *y* = (2/3)*x* + 30, *y* = (−2/3)*x* + 50, *y* = −2*x* + 30 and *y* = 2*x* – 30. How many square units are in the area of Molly’s design?

## Combining Shapes

The radius of circle N is 3 inches, and the radius of circle O is 4 inches. What is the radius of circle P whose area is the sum of the areas of circles N and O?

## Space Junk

Space junk is debris orbiting Earth that, for the most part, has been abandoned or has broken off spacecrafts and rockets. Some of these items are far enough from Earth that they will remain in orbit forever; however, much of this “junk” will be pulled into Earth’s atmosphere by gravity. On average, one item per day falls victim to gravity. At this rate, in what year will 2500 pieces of space junk enter the atmosphere if we begin counting on February 18th?

## MATHCOUNTS Valentine

On some graph paper, graph the following segments:

*y* = *x*, for 0 ≤ *x* ≤ 2*y* = 2*x* − 2, for 2 ≤ *x* ≤ 3*x* = 3, for 4 ≤ *y* ≤ 6*y* = −*x* + 9, for 2 ≤ *x* ≤ 3*y* = 7, for 1 ≤ *x* ≤ 2*y* = *x* + 6, for 0 ≤ *x* ≤ 1

Now reflect each of the segments over the *y*-axis. What popular shape have you drawn?

## Hot Air Balloons

Fall is a beautiful time of year to take a hot air balloon ride! You may not be able to take a balloon ride, but we hope you enjoy solving this week’s problems.

Melrose’s hot air balloon is a sphere of diameter 100 feet. How many cubic feet of air will Melrose’s hot air balloon hold when completely filled? Express your answer as a decimal to the nearest tenth.