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

Grade 10 Math Worksheet

Circle the best answer.

1. 1.

   Ari's polyhedron has 12 faces, all pentagons. Each edge is shared by two faces. How many vertices does it have?

   • 50
   • 30
   • 20
   • 18
2. 2.

   Bo's polyhedron has 8 faces, all triangles. Each edge is shared by two faces. How many vertices does it have?

   • 6
   • 4
   • 12
   • 18
3. 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?

   • 22
   • 60
   • 24
   • 36
4. 4.

   Jun's clay cube has 6 cm edges. A flat cut passes through two opposite edges. What is the cut face?

   • A square, 6√2 cm by 6√2 cm
   • A rectangle, 6 cm by 12 cm
   • A square, 6 cm by 6 cm
   • A rectangle, 6 cm by 6√2 cm
5. 5.

   Kira cuts a ball of radius 13 cm with a flat cut 5 cm from its center. What is the radius of the circular cut face?

   • 13 cm
   • 12 cm
   • 8 cm
   • 5 cm
6. 6.

   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?

   • 36π cm²
   • 9π cm²
   • 3π cm²
   • 81π cm²
7. 7.

   Milo spins a right triangle with legs 6 cm and 8 cm about the 8 cm leg. What is the volume of the cone it makes?

   • 16π cm³
   • 128π cm³
   • 288π cm³
   • 96π cm³
8. 8.

   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?

   • 280π cm³
   • 112π cm³
   • 343π cm³
   • 406π cm³
9. 9.

   Which shape can NOT be the cut face when Ren makes one flat cut through a solid cylinder?

   • A rectangle
   • A triangle
   • A circle
   • An ellipse
10. 10.

    Which shape can NOT be the cut face when Tala makes one flat cut through a solid cube?

    • A regular hexagon
    • A triangle
    • A heptagon (7 sides)
    • A rectangle that is not a square