Deck 25: Counting Units Fast: Measurement Formulas

Question 1

You would like to buy wheels for your child's go-cart, so that the wheels will roll 1 meter in one full revolution. What should the diameter of each wheel be in centimeters?

Answer 1

31.85 centimeters

Question 2

You would like to buy wheels for your child's go-cart so that the wheels will roll 1 meter in one full revolution. What should the diameter of each wheel be in meters?

A) 0.32 meters
B) 0.56 meters
C) 1.13 meters
D) 0.1 meters
E) 3.14 meters

Answer 2

0.32 meters

Question 3

What is the area of the trapezoid shown below?

Answer 3

14 square centimeters

Question 4

What is the area of a rectangle similar to the one shown with a size change of scale factor 4?

Question 5

What is the area of a rectangle with perimeter 20 meters and base 6 meters?

Question 6

What is the area of a rectangle with perimeter 20 meters and base 6 meters?

A) 120 square meters
B) 60 square meters
C) 160 square meters
D) 24 square meters
E) 84 square meters

Question 7

Explain why a formula for the volume of a prism is the following. (Use a drawing if that is helpful.)
V_prism = (area of the base)(height)

Question 8

Find the approximate volume of the cone with the following dimensions.

Question 9

Find the approximate volume of the cone with the following dimensions.

A) 80 cubic centimeters
B) 20 cubic centimeters
C) 22.75 cubic centimeters
D) 90 cubic centimeters
E) 183.3 cubic centimeters

Question 10

Find an expression for the area of the figure below, in terms of the indicated measurements. (Angles that look like right angles are right angles.)

Question 11

Find the area of the figure, if c = 8 cm, n = 7 cm, and a = 20 cm. (Angles that look like right angles are right angles.)

Question 12

Find the area of the figure below. (Angles that look like right angles are right angles).

A) $n a+\frac{1}{2}(\mathrm{nc})$ square units
B) $n (c-a)+\frac{1}{2}(\mathrm{nc})$ square units
C) $n (c+a)+\frac{1}{2}(\mathrm{nc})$ square units
D) $n (a-c)+\frac{1}{2}(\mathrm{nc})$ square units
E) None of the answers is correct.

Question 13

Explain why a formula for the area of a trapezoid is the following.
A_trap =

Question 14

The lengths of the sides of the triangle below are x, y, and z, and with p as shown. Tell how to use the figure to justify the formula for the area of the triangle, without introducing any new variables. Write enough to make your thinking clear.

Question 15

A regular square pyramid has 2-centimeter edges on its base, and the other edges are 3 centimeters long.

A) Sketch a net for a pyramid that is similar to the one described above, with a scale factor of 1.5. Make sure to label the lengths on your sketch.
B) If the original pyramid has a volume of 3.5 cubic centimeters, what will be the volume of the new pyramid in part A? Show (and explain) your work.

Question 16

An ice cream cone filled just to the top holds 28 cubic centimeters and has a height of 6 centimeters. What is the area of the base of the cone?

A) $\frac { 14 } { 3 }$ square centimeters
B) $2 \sqrt { 14 }$ square centimeters
C) $\sqrt { \frac { 14 } { \pi } }$ square centimeters
D) 14 square centimeters

Question 17

A cylindrical container has a volume of 320 $\pi$
cubic centimeters of water, and the diameter of the container is 8 centimeters. What is the height of the container?

Question 18

Find the area of the triangle.

Question 19

What is the area of the figure below?

Question 20

To the nearest inch, a rectangle measures 2 inches by 4 inches. The area of the rectangle could be anywhere between _____ square inches and _____ square inches. Please express your answer(s) as fractions or mixed numbers.

Question 21

If the diameter of a tennis ball is a little more than 6 centimeters, what is the approximate surface area and volume of the tennis ball?

Question 22

A) Sketch the three-dimensional shape that has the net shown. (The middle part is a rectangle.)
B) Name the three-dimensional shape as fully as possible.
C) Give the volume and surface area of the three-dimensional shape. (Use correct units. Show your work for credit.)

Question 23

The area of the triangle below is 24 square units. Each of the sides in a triangle can be used as a base. For each of the triangles shown, choose a different side as the base and then draw the corresponding height for that base. Find the measurement of that height.

Question 24

What is the area of the circle below?

A) 2.25 $\pi$ square inches
B) 9 $\pi$ square inches
C) 6 $\pi$ square inches
D) 3 $\pi$ square inches
E) 1.5 Square inches $\pi$

Question 25

What is the volume of the box below?

Height of box $= 2.5$ inches
Area of bottom of box $= 35 \mathrm { sq }$ . inches
Length of diagonal of bottom $= 8.5$ inches

A) 87.5 cubic inches
B) 743.75 cubic inches
C) 297.5 cubic inches
D) 46 cubic inches
E) 37.5 cubic inches

Question 26

If the volume of a right circular cylinder with radius 5 centimeters is about 550 cubic centimeters, what is the approximate height of the cylinder?

A) 110 centimeters
B) 35 centimeters
C) 22 centimeters
D) 7 centimeters
E) 3 centimeters

Question 27

The perimeter of a square is 20 centimeters. What is its area in square centimeters?

A) 400
B) 80
C) 25
D) 20
E) None of the answers is correct.

Question 28

What is the area of the triangle below in square centimeters? The given measurements are in centimeters.

A) 32
B) 31
C) 24
D) 16
E) None of the answers is correct.

Question 29

Give the area and the perimeter of the following shape. The curved edges are semicircles with the indicated points as centers.

Question 30

In the shape below, ABCDE is a regular pentagon, M is the midpoint of side AB, and A is the center of the circular arc. Find the area of the shaded shape and the perimeter of the entire shape.

Question 31

In the shape below, the curves are semicircles, with the centers and radii indicated. Find the area and the perimeter of the shape.