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

Grade 10 Math Worksheet - Challenge Me

Circle the best answer.

1. 1.

   Ari spins a right triangle with legs 6 cm and 8 cm about its hypotenuse. What is the volume of the solid?

   • 230.4π cm³
   • 120π cm³
   • 96π cm³
   • 76.8π cm³
2. 2.

   Bo spins the trapezoid in the figure about its vertical side. What is the volume of the solid?

   • 58π cm³
   • 150π cm³
   • 73.5π cm³
   • 78π cm³
3. 3.

   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
   • 8 cm
   • √514 cm
   • 17 cm
4. 4.

   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?

   • 144π cm²
   • 49π cm²
   • 7π cm²
   • 119π cm²
5. 5.

   Milo says a flat cut through a cube can never make a regular hexagon, since a cube's faces are squares. Which verdict is right?

   • Wrong: a plane through the midpoints of six edges crosses all six faces and makes a regular hexagon.
   • Wrong, but only for a cut that passes through a vertex of the cube, and for no other cut.
   • Right: each side of the cut lies in a square face, so every angle of the cut must be a right angle, as in the faces.
   • Right: cube cuts are only triangles, rectangles or squares, so a hexagon is not among them.
6. 6.

   Noah says every flat cut of a solid cone that misses its base is a circle or a triangle. Which verdict is right?

   • Wrong, but an ellipse needs the cut to pass through the tip.
   • 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.
7. 7.

   Pia slices a pyramid with a 7-sided base with one flat cut. What is the most sides the cut face can have?

   • 9
   • 8
   • 6
   • 14
8. 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
   • 150
   • 90
   • 58
9. 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?

   • 30
   • 18
   • 12
   • 10
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
    • 32π cm²
    • (32√3/3)π cm²
    • 8π cm²