Why the volume formulas work (Cavalieri's principle)

Answer Key - Grade 10 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. Read this first

   Sketch, not to scale

   The leaning stack with layers 9 cm by 6 cm, the straight-up height 4 cm, and the slanted edge 5 cm.

2. 1.

   Kira's stack of notebooks has 9 by 6 cm layers and stands 4 cm tall. Pushed so it leans, its slanted edge is 5 cm. What is its volume now, in cubic cm?

   216

3. Sketch, not to scale

   The leaning stack with layers 10 cm by 7 cm, the straight-up height 3 cm, and the slanted edge 5 cm.

4. 2.

   Luz's stack of paper has 10 by 7 cm layers and stands 3 cm tall. Pushed so it leans, its slanted edge is 5 cm. What is its volume now, in cubic cm?

   210
5. 3.

   “Sketch, not to scale:” Milo's tile stack has 8 by 5 cm layers and stands 6 cm tall. Pushed so it leans, its slanted edge is 10 cm. What is its volume now, in cubic cm?

   240
6. 4.

   Noah's stack of game boxes has 12 by 3 inches layers and stands 5 inches tall. Pushed so it leans, its slanted edge is 13 inches. What is its volume now, in cubic inches?

   180
7. 5.

   Pia has two stacks of 20 equal coins. One stands straight; the other leans. How do their volumes compare?

   • The straight stack is bigger.
   • They are equal.
   • You can only tell if both slices are the same shape.
   • The leaning stack is bigger.
8. 6.

   “Sketch:” Ren stacks 12 equal books straight, then twists the next stack of 12 like a fan. How do the two stacks' volumes compare?

   • The twisted stack is smaller.
   • They are equal.
   • You can only tell if the stacks have the same outline.
   • The twisted stack is bigger.
9. 7.

   Tala's two clay towers are 10 cm tall. At every height, one has a square slice of 36 square cm, the other a circle slice of 36 square cm. How do their volumes compare?

   • The round tower is bigger because it leans out.
   • You can't compare a square and a circle.
   • The square tower is bigger.
   • They are equal.
10. 8.

    Zee stacks 8 equal slices of bread straight, and 8 more that slide sideways. How do the two stacks' volumes compare?

    • They are equal.
    • You can only tell if both stacks have the same outline.
    • The sliding stack is bigger.
    • The straight stack is bigger.
11. 9.

    Esme cuts a foam cube with 18 cm edges into 3 equal pyramids, each with a cube face as its base. What is each pyramid's volume, in cubic cm?

    1944
12. 10.

    Jun cuts a foam cube with 21 cm edges into 3 equal pyramids, each with a cube face as its base. What is each pyramid's volume, in cubic cm?

    3087