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

Grade 10 Math Worksheet

Circle the best answer.

1. 1.

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

   • 4
   • 18
   • 12
   • 6
2. 2.

   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 6√2 cm
   • A square, 6 cm by 6 cm
   • A square, 6√2 cm by 6√2 cm
   • A rectangle, 6 cm by 12 cm
3. 3.

   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?

   • 12 cm
   • 13 cm
   • 8 cm
   • 5 cm
4. 4.

   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
   • 36π cm²
   • 9π cm²
   • 81π cm²
5. 5.

   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?

   • 96π cm³
   • 16π cm³
   • 288π cm³
   • 128π cm³
6. 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?

   • 343π cm³
   • 112π cm³
   • 406π cm³
   • 280π cm³
7. 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?

   • 9.6π cm³
   • 15π cm³
   • 12π cm³
   • 28.8π cm³
8. 8.

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

   • A triangle
   • An ellipse
   • A rectangle
   • A circle
9. 9.

   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
10. 10.

    Which shape can NOT be the cut face when Zee makes one flat cut through a solid square pyramid?

    • A hexagon
    • A trapezoid
    • A pentagon
    • A square