Nets, and views of a solid from the top, front and side

Answer Key - Grade 10 Math Worksheet

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

1. 1.

   Ari builds on a 3 by 3 base and records the front and right-side views on the card. What is the greatest number of cubes the building could have?

   14 cubes
2. 2.

   Bo builds on a 3 by 3 base and records the front and right-side views on the card. What is the greatest number of cubes the building could have?

   16 cubes
3. 3.

   Esme builds on a 3 by 3 base and records the front and right-side views on the card. What is the greatest number of cubes the building could have?

   15 cubes
4. 4.

   Kira slices a cone parallel to its base. The base radius is 6 cm, the height is 9 cm, and the cut is 6 cm above the base. What is the cross-section?

   • A circle with a radius of 4 cm
   • A circle with a radius of 6 cm
   • An ellipse with axes of 4 cm and 6 cm
   • A circle with a radius of 2 cm
5. 5.

   Luz slices a cylinder of radius 5 cm and height 12 cm with a vertical plane that is 3 cm from the axis. What is the cross-section?

   • An ellipse with axes of 8 cm and 12 cm
   • A rectangle 10 cm by 12 cm
   • A rectangle 6 cm by 12 cm
   • A rectangle 8 cm by 12 cm
6. 6.

   Milo spins a 3 cm by 5 cm rectangle about its 5 cm side. What solid does it sweep out?

   • A cylinder with radius 3 cm and height 5 cm, volume 15π cm³
   • A cylinder with radius 5 cm and height 3 cm, volume 75π cm³
   • A cone with radius 3 cm and height 5 cm, volume 15π cm³
   • A cylinder with radius 3 cm and height 5 cm, volume 45π cm³
7. 7.

   Pia spins a 2 cm by 6 cm rectangle about a line 1 cm from its long side. The line is parallel to the long side and outside the rectangle. What solid and volume result?

   • A ring-shaped solid, outer radius 3 cm, inner radius 1 cm, height 6 cm, volume 24π cm³
   • A ring-shaped solid, outer radius 7 cm, inner radius 1 cm, height 2 cm, volume 96π cm³
   • A solid cylinder with radius 3 cm and height 6 cm, volume 54π cm³
   • A ring-shaped solid, outer radius 3 cm, inner radius 1 cm, height 6 cm, volume 48π cm³
8. 8.

   Ren says the front and right-side views on the card fix a 3 by 3 building exactly. Which reply is justified?

   • No: between 4 and 10 cubes match both views, so the views do not fix the building
   • Yes: as many as 12 cubes could be hidden behind the taller stacks
   • Yes: exactly 8 cubes, because the front view and the side view are added together
   • Yes: exactly 4 cubes, because each unit of the front view is one cube in a fixed place

9. Read this first

   Use this

   Front view, tallest stack in each column from the left: 1, 3, 2. Right-side view, tallest stack in each row (row 1 on the left): 2, 1, 3.

10. 9.

    Tala says the front and right-side views on the card fix a 3 by 3 building exactly. Which reply is justified?

    • No: between 6 and 14 cubes match both views, so the views do not fix the building
    • Yes: as many as 16 cubes could be hidden behind the taller stacks
    • Yes: exactly 6 cubes, because each unit of the front view is one cube in a fixed place
    • Yes: exactly 12 cubes, because the front view and the side view are added together
11. 10.

    Zee says the front and right-side views on the card fix a 3 by 3 building exactly. Which reply is justified?

    • No: between 8 and 16 cubes match both views, so the views do not fix the building
    • Yes: exactly 13 cubes, because the front view and the side view are added together
    • Yes: as many as 18 cubes could be hidden behind the taller stacks
    • Yes: exactly 7 cubes, because each unit of the front view is one cube in a fixed place