Volume of Right Pyramids

Launch Look for a pattern in the volumes of the prism and pyramid pairs. Find the volume of a fourth pyramid with a base 2 ft by 6 ft and height 3 ft. Explain your reasoning.

Volume of a Pyramid Suppose you have a pyramid and a prism with the same base and the same height. By turning these solid figures into containers you can show a relationship between their volumes. It takes 3 of the pyramid to fill the prism. So the volume of the prism is three times the volume of the pyramid. This means that the volume of the pyramid is 1/3 the volume of the prism. So the volume of a pyramid equals 1/3*Bh.

Find the Volume of each Pyramid. V = 1/3 Bh V = 1/3 (7) (7) (15) V = 735/3 V = 245 in³

Find the Volume of each Pyramid. V = 1/3 Bh V = 1/3 (10) (10) (9) V = 900/3 V = 300 in³

V = 1/3 Bh V = 1/3 (9) (9) (13) V = 1053/3 V = 351 in³

Find the Volume of each Pyramid. Ms. Adventure visited the Mayan pyramids in Mexico. The structure shown approximates a square pyramid with a height of 30 m. What is the approximate volume of the Mayan pyramid? V = 1/3 Bh V = 1/3 (55) (55) (30) V = 90750/3 V = 30250 in³

What happens to the volume of a square pyramid when you double the side length of the base? V = 1/3 Bh V = 1/3 (3) (3) (4) V = 36/3 V = 12 in³ V = 1/3 Bh V = 1/3 (6) (6) (4) V = 144/3 V = 48 in³

Find the Volume of the Pyramid Ms. Adventure’s tea package has the shape of a regular triangular pyramid. To the nearest tenth of a cubic inch, how much tea can the package hold? V = 1/3 Bh V = 1/3 ( 1/2*bh) (h) V = 1/3 ( 1/2 )(1.4) (1.2) (3) V = 5.04/6 V = 0.84 in³ V = 0.8 in³

Find the Volume of the Pyramid To the nearest cubic foot, what is the volume of the regular triangular pyramid?

Find the Volume of the Pyramid Ms. Adventure’s tent has the shape of a regular hexagonal pyramid. To the nearest cubic foot, how much space is in the tent? V = 1/3 Bh V = 1/3 (6) ( 1/2 * bh) (h) or (bh) (h) V = 1/3 (6) ( 1/2 )(3.5) (3) (4.7) or (3.5) (3) (4.7) V = 296.1/6 or 49.35 V = 49.35 ft³ V = 49 ft³

Find the Volume of the Pyramid To the nearest cubic foot, what is the volume of the regular hexagonal pyramid? V = 1/3 Bh V = 1/3 (6) ( 1/2 * bh) (h) or (bh) (h) V = 1/3 (6) ( 1/2 )(2) (1.7) (4) or (2) (1.7) (4) V = 81.6/6 or 13.6 V = 13.6 ft³ V = 14 ft³

Close and Check How can you apply what you know about finding the volume of one right square pyramid to find the volume of any right pyramid? You can apply the same formula, V = 1/3 Bh, to find the volume of any right pyramid, but the formula for finding the area of a base (B) will depend on the shape of the base.

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