Q3W5.5 GEO Study Guide #1-15

Q3W5.5 Unit Exam #1-15

Rotating Plane Figures & Cross Sections of Solids

Volume of Solids

Modeling with Volume of Solids

Multiple Choice

1)

​1) solution

Multiple Choice

2)

Multiple Choice

**BONUS**

not on study guide

• triangle

• rectangle

• trapezoid

• parallelogram

• pentagon

​2) solution

Multiple Choice

3) Square JKLM is shown.

Which three-dimensional figure could result from rotating square JKLM 360^o clockwise about the y-axis?

Multiple Choice

4)

• cone

• cylinder

• pyramid

• sphere

​4) solution

Fill in the Blanks

​5) solution

Multiple Choice

6) The volume of a cylinder is 90 cubic centimeters.

Which step can be performed to find the volume of a cone with the same radius and height as the cylinder?

• divide the volume of the cylinder by π

• multiply the volume of the cylinder by 3

• divide the volume of the cylinder by 3

• multiply the volume of the cylinder by 3

​11) solution

Dropdown

**BONUS like 6)**

The volume of a cone is 45 cubic millimeters. To find the volume of a cylinder with the same radius and height as a cone, you would ​

Select answer

the volume of the cone by ​

Select answer

.

​BONUS 6) solution

Multiple Choice

7) A company wants to determine the amount of a vitamin mix that can be enclosed in a capsule like the one shown. The capsule has a radius of 3 millimeters (mm) and a length of 15 mm.

Which statement best explains how to find the amount of vitamin mix that fits in the capsule?

• Add the volume of a sphere with a radius of 3 mm to the volume of a cylinder with a radius of 3 mm and a height of 9 mm.

• Add the volume of a sphere with a radius of 3 mm to the volume of a cylinder with a radius of 3 mm and a height of 15 mm.

• Add the volume of a sphere with a radius of 6 mm to the volume of a cylinder with a radius of 6 mm and a height of 9 mm.

• Add the volume of a sphere with a radius of 6 mm to the volume of a cylinder with a radius of 6 mm and a height of 15 mm.

Multiple Choice

**BONUS like 7)**

A company wants to determine the amount of a vitamin mix that can be enclosed in a capsule like the one shown. The capsule has a diameter of 4 millimeters (mm) and a length of 15 mm.

Which statement best explains how to find the amount of vitamin mix that fits in the capsule?

• Add the volume of a sphere with a radius of 4 mm to the volume of a cylinder with a radius of 4 mm and a height of 15 mm.

• Add the volume of a sphere with a radius of 4 mm to the volume of a cylinder with a radius of 4 mm and a height of 11 mm.

• Add the volume of a sphere with a radius of 2 mm to the volume of a cylinder with a radius of 2 mm and a height of 15 mm.

• Add the volume of a sphere with a radius of 2 mm to the volume of a cylinder with a radius of 2 mm and a height of 11 mm.

Match

8)

• radius: 3.5 cm

• radius: 4

• radius: 4.5

• radius: 5 cm

• radius 5.5

too small for constraints

height: 9.5 cm

height: 7.5 cm

height: 6.1

too big for constraints

• too small for constraints

• height: 9.5 cm

• height: 7.5 cm

• height: 6.1

• too big for constraints

​8) solution

STEP 1: STEP 2: STEP 3:

Fill in the Blanks

​BONUS 8) solution

Fill in the Blanks

​9) solution

Match

Match the following:

• A. original

• A. simplified

• B. Length of Base

• B. Height of Triangular Face

1000 = 1/3(8y)²(3y)

1000/64 = y³

10/4 = y

2.5 = y

20

12.5

• 1000 = 1/3(8y)²(3y)

• 1000/64 = y³

  10/4 = y

  2.5 = y

• 20

• 12.5

​10) solution

A. A. B. B.

original simplified Length of Base Height of Trianglular Face

Match

11) A company wants to design a cylindrical object that has a height of 10 centimeters and a volume of at least 2,000 cubic centimeters, but not more than 2,500 cubic centimeters.

What is a possible radius, in centimeters, of the cylinder? Round your answer to the nearest hundredth.

_______ centimeters

• V = 1750 cm³

• V = 2000 cm³

• V = 2250 cm³

• V=2500 cm³

• V = 2750 cm³

too small for constraints

r= 7.979 cm

r= 8.463 cm

r= 8.921 cm

too big for constraints

• too small for constraints

• r= 7.979 cm

• r= 8.463 cm

• r= 8.921 cm

• too big for constraints

​11) solution

Fill in the Blanks

​12) solution

Fill in the Blanks

​BONUS 12) solution

Dropdown

13) The area of a cross section parallel to the base at the same height in each cone is ​ ​

Select answer

.

Therefore, the volume of Cone 1 is ​

Select answer

the volume of Cone 2.

​13) solution

Match

14)

Match the following

• if r_cone = r_sphere

  _{radius of cone:}

  _{24 units}

• if r_cone > r_sphere

  _{radius of cone:}

  _{30 units}

• if r_cone < r_sphere

  _{radius of cone:}

  _{20 units}

radius of sphere:

24 units

radius of sphere:

27.85 units

radius of sphere:

21.253 units

• radius of sphere:

  24 units

• radius of sphere:

  27.85 units

• radius of sphere:

  21.253 units

​14) solution

1. sphere radius = cone radius 2. sphere radius > cone radius 3. sphere radius < cone radius

​14) solution

​BONUS 14) solution