Resources

Resources

Pythagorean Theorem and its converse

Li Wei usually gets to work by walking

1

3

12^{\text {th }}

Street and then turning right

90^{\circ}

and walking east on Azalia Street for

3

3

miles. His friend mentions that Li Wei could take Washington Street instead, which goes directly from his apartment to his workplace, in a straight line. Approximately how much shorter, in miles, is this route compared to

\mathrm{Li}

Wei's usual walking route?

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(Round your answer to the nearest tenth of a mile.)

A cylinder and cone have equal volumes and radii of equal length. If the height of the cone is

24

centimeters, then what is the height of the cylinder in centimeters?

A park shaped like a pentagon has four equal length sides and one unequal side whose length is

35

(\mathrm{ft})

. The perimeter of the park is

195 \mathrm{ft}

. What is the length in feet of one of the equal length sides?

The length of a rectangular swimming pool is twice as long as its width. If the perimeter of the pool is

120

feet, then what is the width of the pool, in feet?

The perimeter of a rectangular movie screen at a local cinema is

148

feet. If the length of the screen is

30

feet longer than the width, what is the length of the screen, in feet?

A household aquarium tank in the shape of a rectangular prism has a base length of

24

inches (in) and a base width of

15 \mathrm{in}

. The height of the water is

12

in above the base. During cleaning,

900

cubic inches of water is removed. What is the absolute value of the change in the height of the water in inches?

An orange is in the shape of a sphere. Its volume is

288 \pi

cubic centimeters. What is the radius of the orange, in centimeters?

A miniature basketball in the shape of a sphere has a volume of approximately

113

cubic inches. What is the length of the basketball's radius, rounded to the nearest inch?

Janine works at a factory and is filling cylindrical molds with molten plastic. It takes

9

6

cubic centimeters of molten plastic to fill the molds to a height of

0

8

centimeters. To the nearest whole centimeter, what is the radius of the cylindrical mold?

Kimi's school is

15

kilometers west of her house and

8

kilometers south of her friend Franklin's house. Every day, Kimi bicycles from her house to her school. After school, she bicycles from her school to Franklin's house. Before dinner, she bicycles home on a bike path that goes straight from Franklin's house to her own house. How far does Kimi bicycle each day?

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