Solution Calculate the height of the pyramid. Let feet represent the height. h In CD is the side length of the base, so CD = 1 ft. ∆ACD, Use the Pythagorean Theorem in to calculate h. ∆ACD + 12 = 72 Solve the equation for h2 h2. + 1 = 49 h2 = 49 1 h2 – = 48 Solve the equation for h2 h. h = The height is ft. Use the formula for the volume of a right pyramid: Volume = (base area)(height) = (2)2() V = 9.2376… V The volume of the pyramid is approximately 9 cubic feet. 2. Determine the volume of a right rectangular pyramid with base dimensions 3.6 m by 4.7 m and height 6.9 m. Answer to the nearest tenth of a cubic metre. Solution Sketch and label a diagram. Use the formula for the volume of a right rectangular pyramid. = Substitute: = 3.6, = 4.7, = 6.9 V lwh l w h = (4.7)(3.6)(6.9) V = 38.916 V The volume of the pyramid is approximately 38.9 m3.
Solution Calculate the height of the pyramid. Let h feet represent the height. In ∆ACD, CD is the side length of the base, so CD = 1 ft. Use the Pythagorean Theorem in ∆ACD to calculate h. h2 + 12 = 72 Solve the equation for h2. h2 + 1 = 49 h2 = 49 – 1 h2 = 48 Solve the equation for h. h = The height is ft. Use the formula for the volume of a right pyramid: Volume = (base area)(height) V = (2)2() V = 9.2376… The volume of the pyramid is approximately 9 cubic feet. 2. Determine the volume of a right rectangular pyramid with base dimensions 3.6 m by 4.7 m and height 6.9 m. Answer to the nearest tenth of a cubic metre. Solution Sketch and label a diagram. Use the formula for the volume of a right rectangular pyramid. V = lwh Substitute: l = 3.6, w = 4.7, h = 6.9 V = (4.7)(3.6)(6.9) V = 38.916 The volume of the pyramid is approximately 38.9 m3.
miap_ch_1_notes_answer_key.docx