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

NameDate

Circle the best answer.

1.
Ari's polyhedron has 12 faces, all pentagons. Each edge is shared by two faces. How many vertices does it have?
- 18
- 30
- 20
- 50
2.
Bo's polyhedron has 8 faces, all triangles. Each edge is shared by two faces. How many vertices does it have?
- 18
- 6
- 4
- 12
3.
Esme's polyhedron has 6 octagon faces and 8 triangle faces. Each edge is shared by two faces. How many vertices does it have?
- 60
- 22
- 24
- 36
4.
Jun's clay cube has 6 cm edges. A flat cut passes through two opposite edges. What is the cut face?
- A rectangle, 6 cm by 12 cm
- A square, 6 cm by 6 cm
- A rectangle, 6 cm by 6√2 cm
- A square, 6√2 cm by 6√2 cm
5.
Luz's cone has base radius 9 cm and height 12 cm. A flat cut parallel to the base is 4 cm below the tip. What is the area of the cut face?
- 3π cm²
- 9π cm²
- 36π cm²
- 81π cm²
6.
Noah spins a rectangle, 4 cm wide and 7 cm tall, about a vertical line 3 cm to its left. What is the volume of the solid?
- 112π cm³
- 406π cm³
- 280π cm³
- 343π cm³
7.
Pia spins a right triangle with legs 3 cm and 4 cm (hypotenuse 5 cm) about its hypotenuse. What is the volume of the solid?
- 12π cm³
- 15π cm³
- 28.8π cm³
- 9.6π cm³
8.
Which shape can NOT be the cut face when Ren makes one flat cut through a solid cylinder?
- A triangle
- A circle
- A rectangle
- An ellipse
9.
Which shape can NOT be the cut face when Tala makes one flat cut through a solid cube?
- A regular hexagon
- A heptagon (7 sides)
- A triangle
- A rectangle that is not a square
10.
Which shape can NOT be the cut face when Zee makes one flat cut through a solid square pyramid?
- A hexagon
- A pentagon
- A trapezoid
- A square

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

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