Square-based pyramids: volume and surface area

Answer Key - Grade 8 Math Worksheet - Building Confidence

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

2. 1.

   Ren makes a square pyramid roof for a model castle tower. A square prism with the same base and height holds 225 cubic inches. What is the pyramid's volume, in cubic inches?

   75
3. 2.

   Tala makes a paper pyramid. A square prism with the same base and height holds 588 cubic cm. What is the pyramid's volume, in cubic cm?

   Use the picture in question 1.

   196
4. 3.

   Zee makes a glass pyramid paperweight. A square prism with the same base and height holds 432 cubic cm. What is the pyramid's volume, in cubic cm?

   Use the picture in question 1.

   144
5. 4.

   Ari unfolds a paper pyramid: a square base of 64 square cm and four triangles of 48 square cm each. What is its surface area, in square cm?

   256
6. 5.

   Bo unfolds a model castle roof: a square base of 100 square inches and four triangles of 65 square inches each. What is its surface area, in square inches?

   360
7. 6.

   Esme unfolds a small pyramid model: a square base of 36 square cm and four triangles of 39 square cm each. What is its surface area, in square cm?

   192
8. 7.

   Jun unfolds a pyramid gift box made of card: a square base of 144 square cm and four triangles of 102 square cm each. What is its surface area, in square cm?

   552
9. 8.

   Kira measures a pyramid sculpture in the park. Its height, 2.1 meters, and half its base, 2 meters, are the legs of a right triangle inside. How long is the slant height, in meters?

   2.9
10. 9.

    Luz measures a tall castle tower roof. Its height, 30 cm, and half its base, 12.5 cm, are the legs of a right triangle inside. How long is the slant height, in cm?

    32.5
11. 10.

    Milo measures a pyramid model for the school hall. Its height, 3 feet, and half its base, 1.25 feet, are the legs of a right triangle inside. How long is the slant height, in feet?

    3.25