Grade 10 · Math · Geometry

10th grade Faces, edges and vertices, slices of solids, and solids made by spinning a shape worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Faces, edges and vertices, slices of solids, and solids made by spinning a shape

Grade 10 Math Worksheet - Building Confidence

NameDate

Circle the best answer.

1.
Ari's paper model has 14 faces and 24 edges. Using V − E + F = 2, how many vertices does it have?
- 36
- 10
- 12
- 8
2.
Bo's gift box has 10 faces and 24 edges. Using V − E + F = 2, how many vertices does it have?
- 32
- 12
- 16
- 14
3.
Esme's tent has 6 vertices and 9 edges. Using V − E + F = 2, how many faces does it have?
- 13
- 5
- 1
- 3
4.
Kira's sand pyramid has 10 vertices. How many edges does it have?
- 27
- 9
- 20
- 18
5.
Luz's gift box is a prism with 14 vertices. How many faces does it have?
- 9
- 7
- 8
- 16
6.
Milo's cone-shaped party hat has base radius 6 cm and height 8 cm. A flat cut parallel to the base is 4 cm above it. What is the radius of the cut?
- 6 cm
- 3 cm
- 12 cm
- 4 cm
7.
Noah's sand pyramid has a square base, 10 cm on a side. A flat cut parallel to the base goes halfway up. What is the cut face?
- A triangle with a 5 cm base
- A square, 5 cm on each side
- A square, 10 cm on each side
- A rectangle, 5 cm by 10 cm
8.
Pia's can is a cylinder with radius 3 cm and height 10 cm. A flat cut parallel to the circular ends goes through the middle. What is the area of the cut face?
- 90π cm²
- 9π cm²
- 6π cm²
- 3π cm²
9.
Tala spins a right triangle with legs 4 cm and 6 cm about the 6 cm leg. Which solid does it make?
- A cone, radius 4 cm and height 6 cm
- A cylinder, radius 4 cm and height 6 cm
- A cone, radius 6 cm and height 4 cm
- A cone, radius 8 cm and height 6 cm
10.
Zee spins a half-circle of radius 5 cm about its straight edge, the diameter. Which solid does it make?
- A sphere, radius 10 cm
- A sphere, radius 5 cm
- A cylinder, radius 5 cm and height 10 cm
- A hemisphere, radius 5 cm

10th grade Faces, edges and vertices, slices of solids, and solids made by spinning a shape worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Faces, edges and vertices, slices of solids, and solids made by spinning a shape. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can use Euler's formula V − E + F = 2 to find a missing count, and work back from a clue to the base of a prism or pyramid.
I can find the size of a cut face (parallel cut of a cone, off-center cut of a ball, tilted cut of a cylinder) and say which shapes a cut can and cannot make.
I can find the volume of a solid made by spinning a triangle, a rectangle away from the axis, or a square about a diagonal.

Standard: G-GMD.B.4

Words to know

face, edge, vertex: A flat side, a line where two faces meet, a corner.

cross-section (slice): The flat shape left where a straight cut goes through a solid.

solid of revolution: The solid a flat shape sweeps out when it spins around a line.

axis: The line a shape spins around; the side on it is the height.

Common mistakes

Your child left the 2 out of Euler's formula V − E + F = 2. Solve for the missing count and keep the +2.

Your child subtracted 2 instead of adding it when solving V − E + F = 2.

Your child mixed up the signs in Euler's formula. It is V − E + F = 2.

Questions parents ask

What is the most common mistake with faces, edges and vertices, slices of solids, and solids made by spinning a shape?

Your child left the 2 out of Euler's formula V − E + F = 2. Solve for the missing count and keep the +2.

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More geometry

See all Geometry

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