Name ____________ Date _____ Per. _____ Teacher_______________

Review # 4 Formulas and Geometry

1) What is the density of an object if its mass is 400 kilograms and its volume is 16 cubic meters?

D = mv

2) Gilda’s family goes on vacation. They travel 120 miles in the first 2 hours. If Gilda’s family continues to travel at this rate, how many miles will they travel in 5 hours?

D = r t

3) The circumference of a circle is 28 π cm. What is the radius of this circle? C = 2r

4) What is the diameter of a circle with a circumference of 40π m? C = 2r

5) The area of circle is 169π cm2. What is the radius of this circle? A = r2

1) The circumference of the circle below is 37.68 centimeters.

Which is the best estimate for the length of the radius of the circle?

a) 6 centimetersb) 12 centimeters

Evaluating Formulas A formula is an equation that expresses a relationship between two or more

variables. Solving a formula

o Identify the correct formula – located on the reference sheet or in the word problem

o Substitute the known values into the formulao Solve for the missing value

c) 18 centimetersd) 24 centimeters

2) What is the volume of the cylinder below?

a) 80 cubic inchesb) 160 cubic inchesc) 400 cubic inchesd) 1,600 cubic inches

3) What is the circumference in terms of ?

a) 20 feetb) 40 feetc) 200 feetd) 400 feet

4) Jamie created a map for his friends. Each point on the map represents a different location.

What coordinates represent Jamie’s house?

a) (2, 3) b) (3, 2) c) (3, 4) d) (4, 3)

C = 2πr

6ft 6ft

4ft

h = 4 m

9 m

15 m

5) A shape is shown below.

What is the best name for this shape?

a) Triangular prismb) Triangular pyramidc) Square prismd) Square pyramid

6) How many faces does the following prism have?

a) 6b) 5c) 4d) 3

7) What is the area of the rectangle drawn on the coordinate plane below?

a) 21 square unitsb) 24 square unitsc) 28 square unitsd) 32 square units

8) All the figures below are prisms except for which figure?

9) Identify the three-dimensional figure that can be formed from this net.

a) cubeb) conec) rectangular pyramidd) cylinder

10) All the figures below are circular except?

11) Richard’s tent is a triangular prism, as shown below. Which combination of shapes makes up the bases and faces of Richard’s tent?

a) 2 triangles, 4 rectanglesb) 2 triangles, 3 rectanglesc) 3 triangles, 2 rectanglesd) 3 triangles, 3 rectangles

12) A circle has a circumference that measures 18 inches. What is the radius, in inches, of the circle?

a) 6b) 9c) 18d) 36

13) A circular camera lens has an area of about 196 square centimeters. What is the radius of the camera lens?

a) 14 centimetersb) 28 centimetersc) 13 centimetersd) 26 centimeters

A = π r2

Part II: Calculators permitted.

14) Joel wants to decorate his pencil case. He must calculate the surface area of the case to determine how much material he needs. A diagram of the pencil case is shown below.

Part A: How much decoration does Joel need in order to cover his case? Round your answer to the nearest tenth of a square centimeter. Show your work.

Answer _______________ square centimeter

Part B: One roll of decorations will cover 125 square centimeters. How many rolls of decorations must Joel buy to cover his entire pencil case?

Answer _______________ rolls of decorations

15) Rashid needs to buy some wood to build a box. He must calculate the surface area of the box to determine how much wood to buy. A diagram of the box is shown below.

Part a: About how much wood does Rashid need to buy to build the box? Show your work.

Answer _______________ square inches

Part B: About how much volume can the box hold?

Answer: _______________ in3 of space

16) A large water tank in the shape of a right circular cylinder stands 25 meters high and measures 15 meters in diameter.

Part AWhat is the volume of the water tank in cubic meters? Round your answers to the nearest cubic meter. Show your work.

Volume __________ m3

Part BFor every cubic meter, the tank can hold 1,000 liters of water. What is the maximum number of liters of water the tank can hold?

Answer __________ liters

17) Dante wants to paint his box. He must calculate the surface area of the box to determine how much paint to buy. A diagram of the box is shown below.

Part a: How much paint does Dante need to buy to paint the box?

Show your work.

Answer _______________ square meters

Part B: How much volume can the box hold?

Answer: _______________ m3 of space

4 m

not drawn to scale

8 m

6m

11 m

10 m

not drawn to scale

5 in.

35 in.

25 in. 100 in. 20 ft

6 ft

8 ft

18) Tiffany wants to paint her toy chest, but first she must calculate the surface area of the chest to find out how much paint she needs. A diagram of the toy chest is shown below.

Part A: How much paint does Tiffany need to paint her toy chest?Show your work.

Answer _______________ square meters

Part B: How much volume can the toy chest hold?

Answer: _______________ m3 of space

19) The YMCA is tiling a new pool. They need to know the surface area of the outside of the pool shown below.

Part ACalculate the surface area, in square feet, of the outside of the pool using the formula: wl + 2lh + 2wh. Show your work.

Answer ______________ square feetPart BExplain why the formula wl + 2lh + 2wh is used to find the surface area of the outside of the pool instead of 2wl + 2lh + 2wh.

Answer ______________