Download Unit 5 Study Guide MCC7.G.4 Know the formula for the area of a

Unit 5 Study Guide
MCC7.G.4 Know the formula for the area of a circle and use them to solve problems; give an informal
derivation of the relationship between the circumference and area of a circle.
MCC7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two
and three dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms .
Formulas:
Circumference = 2𝜋r or 𝜋𝑑
Area of a Circle = 𝜋𝑟 2
Area of Rectangle = bh
Area of Parallelogram = bh
1
Area of Triangle = 2 𝑏ℎ
Area of Trapezoid = 1/2 h (b1 + b2)
1
Volume of Prism = Bh (B = area of base)
Volume of Pyramid = 𝐵ℎ (B = area of base)
3
Surface Area of Prism and Pyramid = Find the area of each side, then add them all together.
Use the figure to the right to answer questions 1 & 2.
1. What is the measure of <GAH? Write an equation and solve.
2. What is the measure of <SAF? Write an equation and solve.
3. The measure of angle XYZ is 132°. Angle ABC and angle XYZ are vertical angles. What
is the measure of angle ABC?
4. <ABC and <CBD are supplementary. <ABC is twenty more than three times <CBD.
Write an equation to find the measure of each angle. Then solve.
5. A triangle can have which of the following sets of sides? Why?
a. 15, 25, 45
b. 4, 12, 18
c. 1, 10, 20
d. 6, 9, 14
6. Using your answer in question 5, how many triangles can those side lengths make?
7. If a triangle has side lengths of 8 and 9, what are the possibilities for the third side?
8. A triangle could have which of the following sets of angles? Why?
a. 80°, 80°, 80° b. 65°, 35°, 80°
c. 90°, 100°, 45°
d. 50°, 45°, 65°
9. Using your answer in question 8, how many triangles can those side lengths make?
10. The Belknap shield volcano is located in the Cascade Range in Oregon. The volcano is
circular and has a diameter of 5 miles. What is the circumference of this volcano?
11. The bottom of a circular swimming pool with a radius of 15 feet is painted blue. How
many square feet are blue?
12. A circle has a circumference of 20.1 inches. What is the area of the circle?
13. The kite is in the shape of a parallelogram. Find the
area of the kite.
14. Ansley is going to help his father shingle the roof of their house. What is the area of the
triangular portion of one end of the roof?
15. In the National Hockey League, goaltenders can play the puck
behind the goal line only in a trapezoid-shaped area, as shown at
the right. Find the area of the trapezoid.
The diagram to the right shows one wall of Sadie’s living room.
16. This wall needs to be painted. Find the total area to be painted.
17. Each quart of paint costs $8 and covers 90 square feet. Find the total cost to paint this
wall once.
18. A toy company makes rectangular sandboxes that measure 4 feet by 7 feet by 1.5 feet .A
customer buys a sandbox and 40 cubic feet of sand. Did the customer by too much or too
little sand?
19. A glass pyramid has a height of 4 inches. Its rectangular base has a length of 3 inches and
a width of 2.5 inches. Find the volume of glass used to create the pyramid.
20. The attic shown is a triangular prism. Insulation will be placed
inside all walls, not including the floor. Find the surface area that
will be covered with insulation.
21. Which cross-sectional shape is common to all three-dimensional pyramids?
22. Which solid figure can have only triangles for cross-sections?
a.
b.
C.
D.
23. Suppose a cylinder is cut by a plane. Which cross-section is NOT possible?
A. Circle
B. Ellipse
C. Square
D. Triangle
24. The cross-section of a three-dimensional figure is shaped like a triangle. The threedimensional figure could NOT be a __________.
A. Cone
B. Cylinder
C. Pyramid
D. Prism
25. A cube is cut by a plane to form a cross-section shaped like a triangle. How could the
plane that formed the cross-section have cut the cube?
A.
B.
C.
D.
parallel to a base of the cube
perpendicular to a base of the cube
slightly tilted away from a base of the cube
none of the above