Faces, edges and vertices, slices of solids, and solids made by spinning a shape
Grade 10 Math Worksheet - Challenge Me
Circle the best answer.
Ari spins a right triangle with legs 6 cm and 8 cm about its hypotenuse. What is the volume of the solid?
- 76.8π cm³
- 230.4π cm³
- 96π cm³
- 120π cm³
Bo spins the trapezoid in the figure about its vertical side. What is the volume of the solid?
- 58π cm³
- 78π cm³
- 73.5π cm³
- 150π cm³
Esme spins a square with 4 cm sides about one of its diagonals. What is the volume of the solid?
- (64√2/3)π cm³
- (32√2/3)π cm³
- 32√2π cm³
- 64π cm³
Jun cuts a ball of radius 10 cm with a flat cut 6 cm from its center. What is the area of the circular cut face?
- 136π cm²
- 16π cm²
- 64π cm²
- 100π cm²
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?
- 7π cm²
- 144π cm²
- 119π cm²
- 49π cm²
Noah says every flat cut of a solid cone that misses its base is a circle or a triangle. Which verdict is right?
- Right: the cone's outline has only a round face and a triangle, so cuts match those.
- Wrong, but an ellipse needs the cut to pass through the tip.
- Right: parallel cuts make circles and cuts through the tip make triangles, so no others exist.
- Wrong: a tilted cut that crosses the slanted side all the way around makes an ellipse.
Pia slices a pyramid with a 7-sided base with one flat cut. What is the most sides the cut face can have?
- 14
- 9
- 8
- 6
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?
- 58
- 150
- 60
- 90
Tala's polyhedron has 4 triangle faces and 4 hexagon faces. Each edge is shared by two faces. How many vertices does it have?
- 18
- 12
- 10
- 30
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?
- (32√3/3)π cm²
- 16π cm²
- 8π cm²
- 32π cm²