Arc Length and Sector Area

Skateboarding has become a popular sport. The Parks Department is thinking of constructing ramps at some of the local playgrounds. The structure has two straight ramps, each of which is 4 feet high and 10 feet long, with a flat space of 20 feet in between. Find the distance a skater travels from the top of one ramp to the top of the other—from point P to point R. (Hint: Use the Pythagorean Theorem. Round your answer to the nearest tenth.)

Tags

CCSS.8.G.B.8

A half-pipe is formed by two quarter-circle ramps, each of which is 10 feet high, plus flat space 20 feet long between the centers. Find the distance a skater travels from the top of one ramp to the top of the other. (Use 3.14 for π. Round your answer to the nearest tenth.)

Tags

CCSS.HSG.C.B.5

Another launch ramp is formed by two arcs, each with a central angle of 60 degrees and a radius of 10 feet, with a flat space of 20 feet between them. Find the length from the top of one ramp to the top of the other. (Hint: What fractional part of the circle is each arc? Use 3.14 for π. Round your answer to the nearest tenth.)

Tags

CCSS.HSG.C.B.5

You have a cake that is 10 inches in diameter. You expect 12 people to share it, so you cut it into 12 equal slices (Figure A). Find the area of each slice of cake. (Use 3.14 for π. Round your answer to the nearest hundredth and write the number only, no units.)

Tags

CCSS.HSG.C.B.5

Before you get a chance to serve the cake, 12 more people arrive! You decide to cut a concentric circle in the cake so that you will have 24 pieces (Figure B). How far from the center of the cake should the circle cut be made so that all 24 people get the same amount of cake? (Use 3.14 for π. Round your answer to the nearest hundredth and write the number only, no units.)

Tags

CCSS.HSG.C.B.5

What is the area of each slice of cake? (Use 3.14 for π. Round your answer to the nearest hundredth and write the number only, no units.)

Tags

CCSS.HSG.C.B.5