Area and Volume Geometry Problems

Geometry

3-D shapes: Volume & Surface Area

Students will be able to:

● Recognize solid shapes (rectangular

prism, cylinder, cone, sphere &
triangular prism).

● Find the surface area of 3D shapes.
● Find the volume of 3D shapes using

the appropriate geometric formula.

● Solve problems concerning real-world

situations with surface area and volume.

● Collaborate with peers to solve geometric

problems for surface area and volume.

5.MD.4, 5.MD.5, 7.G.6, G.CO.1, G.GMD.3

Focus Standard

MP.1 “Make sense of problems and
persevere in solving them.”

6.G.4 “Practice finding the surface
area of 3D objects.”

G.GMD.3

“Use volume formulas for
cylinders, pyramids, cones, and
spheres to solve problems.”

Formulas Needed!

Open Ended

This formula is used to find the ___________ of a cone: $$\frac{1}{3}\pi r^2h$$

Open Ended

This formula is used to find the ___________ of a right prism: $$ph+2B$$

Watch the video linked below.

​Math Antics Volume Cut Edition

https://youtu.be/KxfEqz-njKI

Volume:

Cylinder, Cone, Rectangular Prism, Sphere

Draw

Draw a cylinder.

Draw

Draw a cone.

Draw

Draw a rectangular prism.

Draw

Draw a cube.

Draw

Draw a sphere.

Rectangular Prisms or Cubes

Formula for Volume:

V = LWH

Solve:

V = (15)(10)(8) = 1,200

Multiple Choice

What is the volume of a rectangular prism that has a length of 25 inches, width of 12 inches, and a height of 9 inches?

• 2200 $$in^3$$

• 2500 $$in^3$$

• 1950 $$in^3$$

• 2700 $$in^3$$

Rectangular Prisms or Cubes

Formula for Volume:

V = LWH or s

Open Ended

What shape is described in the following statement?

What is the volume of a box that has a length of 4 feet, a width of 4 feet, and a height of 4 feet

Cones

Formula for Volume:

V = r h

We will use 3.14 for

200.96

​200.96

Cones

We will use 3.14 for

​339.12

Multiple Choice

What is the volume of a cone with a radius of 7 centimeters and a height of 14 centimeters? Use 3.14 for $$\pi$$ . Round the answer to the nearest hundredth.

• 718.10 $$cm^3$$

• 718.01 $$cm^3$$

• 718.22 $$cm^3$$

• 718.02 $$cm^3$$

Cylinders

Formula for Volume:

V = r h

Multiple Choice

What is the volume of a cylinder with a radius of 8 inches and a height of 13.5 inches? Use 3.14 for $$\pi$$ . Round your answer to the nearest whole inch.

• 2713 $$inches^3$$

• 2712 $$inches^2$$

• 2712.9 $$inches^3$$

• 2712.96 inches

Watch the video linked below.

​Nerdstudy: Surface Area & Volume of Prisms

https://youtu.be/7_ZNR2s3JJc

Surface Area:

Cylinder, Cone, Rectangular Prism, Sphere

Open Ended

What shape is described in the following statement?

A farmer stores his grain in a silo that has a radius of 15 feet and a height of 50 feet.

Open Ended

What shape is described in the following statement?

A basketball has a radius of 4.8 inches.

Open Ended

What shape is described in the following statement?

A birthday party hat that has a radius of 4.5 inches and a height of 8.4 inches.

Rectangular Prisms

Formula for Surface Area:
SA = 2LW + 2LH + 2WH

Solve:

SA = 2(15)(10) + 2(15)(8) + 2(10)(8) =700

Rectangular Prisms

Formula for Surface Area:
SA = 2LW + 2LH + 2WH

Solve:

SA = 2(25)(15) + 2(25)(11) + 2(15)(11) =1630

Multiple Choice

What is the surface area of a rectangular prism that has a length of 9 inches, a width of 6 inches, and a height of 4 inches?

• $$228\ in^3$$

• $$228\ in$$

• $$228\ in^2$$

• $$228$$

Cones

Formula for Surface Area:

SA = rs + r

Solve:

SA = (3.14)(4)(12.6) + (3.14)(4)^2 = 208.5

We will use 3.14 for

We will use Pythagorean
Theorem to find the slant
height.

Multiple Choice

Find the slant height of a cone that has a radius of 8 centimeters and a height of 14 centimeters. Hint: Use the formula $$a^2+b^2=c^2$$ . Round the answer to the nearest whole centimeter.

• 16.1 cm

• 15 cm

• 17 cm

• 16 cm

Multiple Choice

Find the surface area of a cone that has a radius of 8 centimeters and a height of 14 centimeters. Hint: Use the formula $$\pi rs+\pi r^2$$ and you found the slant height in the previous problem. Round the answer to the nearest tenth of a centimeter.

• 602.88 $$cm^2$$

• 602.9 $$cm^2$$

• 602.8 $$cm^2$$

• 603 $$cm^2$$

Cylinder

Formula for Surface Area:

SA = 2 rh + 2 r

Solve:

SA = 2(3.14)(2.5)(18) + 2(3.14)(2.5)^2 = 321.85

We will use 3.14 for

Multiple Choice

Find the surface area of a cylinder with a radius of 7 meters and a height of 15 meters. Hint: Use the formula $$2\pi rh+2\pi r^2$$ . Use 3.14 for $$\pi$$ .

• 968 $$cm^2$$

• 967.12 $$cm^2$$

• 967.12 $$cm^3$$

• 968 $$cm^3$$

Sphere

Formula for Surface Area:

SA = r

Solve:

SA = (3.14)(115)^2 = 41526.5

We will use 3.14 for

Multiple Choice

What is the surface area of a basketball with a radius of 4.5 inches? Hint: Use the formula: $$\pi r^2$$ . Use 3.14 for $$\pi$$ . Round the answer to the nearest hundredths of an inch.

• 63.59 $$in^2$$

• 63.6 $$in^2$$

• 63.585 $$in^2$$

• 63.59 $$in^3$$

Multiple Choice

Find the volume to the nearest tenth using 3.14 instead of Pi.

• 282.6 in³

• 94.2 in³

• 235.5 in³

• 78.5 in³

Multiple Choice

Find the volume to the nearest hundredth using 3.14 instead of Pi.

• 12.56 ft³

• 37.68 ft³

• 18.84 ft³

• 6.28 ft³

Multiple Choice

 Find the volume of the solid shown in the figure?

• 7230

• 6621

• 1130

• 907

Multiple Choice

What is another word to describe volume?

• Area

• surface area

• capacity

• 4th dimension

Multiple Choice

What is the formula for volume of a CONE?

• V = π r²

• V = π r² h

• V =  ⅓ π r² h

• V =  ⅓ L W H

Multiple Choice

What is the volume formula for a sphere?

• V = (4 ∕ 3)πr³

• V = (1 ∕ 3)πr²h

• V = πr²h

• V = (1 ∕ 3)Bh

Multiple Choice

What is the formula for volume of a CYLINDER?

• V = π r²

• V = π r² h

• V =  ⅓ π r² h

• V =  ⅓ L W H

Multiple Choice

V = 4/3⋅π⋅r³

• Sphere

• Cube

• Triangular Pyramid

• Rectangular Prism

Multiple Choice

Cylinders have ______________.

• a height

• a slant height

• both a height and slant height

• neither a height or slant height

Multiple Choice

Cones have ______________.

• a height

• a slant height

• both a height and slant height

• neither a height or slant height

Multiple Choice

The slant height of the cone is _______

• $$\overline{DE}$$

• $$\overline{DG}$$

• $$\overline{FE}$$

• $$\overline{GF}$$

Multiple Choice

The height of the cone is _______

• $$\overline{DE}$$

• $$\overline{DG}$$

• $$\overline{FE}$$

• $$\overline{GF}$$

Multiple Choice

Campbell Soup is creating a new soup label. If a can has a height of 6 in and a diameter of 4 in, how much material does Campbell need for each soup label? Use 3.14 for π.

What is the surface area of the label?

• 150.72 in²

• 100.48 in²

• 24 in²

• 75.36 in²

Multiple Choice

A paper party hat, like the one shown, has a slant height of 6 inches and a height of 5 inches. How many square feet of cardboard would be needed to create this hat?

• 62.5 in.²

• 10 in.²

• 50 in.²

• 22.5 in.²

I CAN...

● Recognize solid shapes (cylinder,

pyramid, cone, & sphere)

● Find the surface area of 3D shapes
● Find the volume of 3D shapes using

the appropriate geometric formula

● Solve problems concerning real-world

situations with surface area and volumes
of cones, cylinders, and spheres

5.MD.4, 5.MD.5, 7.G.6, G.CO.1, G.GMD.3

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