Grade 10 · Math · Geometry

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

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

Grade 10 Math Worksheet - Challenge Me

NameDate

Circle the best answer.

1.
Ari spins a right triangle with legs 6 cm and 8 cm about its hypotenuse. What is the volume of the solid?
- 120π cm³
- 230.4π cm³
- 96π cm³
- 76.8π cm³
2.
Bo spins the trapezoid in the figure about its vertical side. What is the volume of the solid?
- 150π cm³
- 58π cm³
- 73.5π cm³
- 78π cm³
3.
Esme spins a square with 4 cm sides about one of its diagonals. What is the volume of the solid?
- (32√2/3)π cm³
- 64π cm³
- 32√2π cm³
- (64√2/3)π cm³
4.
Kira's flat cut of a ball makes a circle of radius 15 cm. The ball's radius is 17 cm. How far is the cut from the ball's center?
- 2 cm
- √514 cm
- 17 cm
- 8 cm
5.
Luz cuts a ball of radius 13 cm twice on the same side of its center, 5 cm and 12 cm from it. How much greater is the first cut face's area?
- 49π cm²
- 119π cm²
- 144π cm²
- 7π cm²
6.
Noah says every flat cut of a solid cone that misses its base is a circle or a triangle. Which verdict is right?
- Right: the cone's outline has only a round face and a triangle, so cuts match those.
- Wrong: a tilted cut that crosses the slanted side all the way around makes an ellipse.
- Right: parallel cuts make circles and cuts through the tip make triangles, so no others exist.
- Wrong, but an ellipse needs the cut to pass through the tip.
7.
Pia slices a pyramid with a 7-sided base with one flat cut. What is the most sides the cut face can have?
- 6
- 9
- 8
- 14
8.
Ren's soccer ball pattern has 12 pentagons and 20 hexagons. Each edge is shared by two panels. How many corners (vertices) does it have?
- 60
- 90
- 58
- 150
9.
Tala's polyhedron has 4 triangle faces and 4 hexagon faces. Each edge is shared by two faces. How many vertices does it have?
- 12
- 18
- 30
- 10
10.
Zee cuts a cylinder of radius 4 cm with a flat plane tilted 60° from the base, all the way through the sides. What is the area of the cut face?
- 16π cm²
- 8π cm²
- (32√3/3)π cm²
- 32π cm²

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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