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

Grade 10 Math Worksheet - Building Confidence

Circle the best answer.

1. 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. 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. 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. 4.

   Kira's sand pyramid has 10 vertices. How many edges does it have?

   • 27
   • 9
   • 20
   • 18
5. 5.

   Luz's gift box is a prism with 14 vertices. How many faces does it have?

   • 9
   • 7
   • 8
   • 16
6. 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. 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. 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. 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. 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