a) The height of the pyramid from which the frustum was cut from. b) The surface area of the frustum

You're on a roll — a) The height of the pyramid from which the frustum was cut from. Step 1: Identify the dimensions. Let H be the height of the original large pyramid and h_s be the height of the small pyramid that was cut off. The height of the frustum is h = 60 cm. The side length of the bottom base of the frustum (and the large pyramid) is L_1 = 40 cm. The side length of the top base of the frustum (and the small pyramid) is L_2 = 20 cm. The height of the large pyramid is H = h_s + h. Step 2: Use similar triangles to find the height H. Consider a cross-section of the pyramid. By similar triangles, the ratio of the heights to the base side lengths (or half-side lengths) is constant: (H)/(L_1) = (h_s)/(L_2) Substitute h_s = H - h: (H)/(L_1) = (H - h)/(L_2) Substitute the given values L_1 = 40 cm, L_2 = 20 cm, and h = 60 cm: (H)/(40) = (H - 60)/(20) Step 3: Solve for H. Multiply both sides by 40: H = 2(H - 60) H = 2H - 120 120 = 2H - H H = 120 cm The height of the pyramid from which the frustum was cut is 120 cm. b) The surface area of the frustum Step 1: Determine the components of the surface area. The frustum is an open container, meaning it has no top base. Its surface area consists of the area of the bottom base and the area of the four trapezoidal lateral faces. Area of bottom base (A_B): A_B = L_1^2 = (40 cm)^2 = 1600 cm^2 Step 2: Calculate the slant height of the frustum (l_f). Consider a right triangle formed by the height of the frustum (h), the difference in half-base lengths, and the slant height of the frustum (l_f). The horizontal leg of this triangle is (L_1 - L_2)/(2) = (40 - 20)/(2) = (20)/(2) = 10 cm. Using the Pythagorean theorem: l_f^2 = h^2 + ((L_1 - L_2)/(2))^2 l_f^2 = (60)^2 + (10)^2 l_f^2 = 3600 + 100 l_f^2 = 3700 l_f = sqrt(3700) = sqrt(100 × 37) = 10sqrt(37) cm Step 3: Calculate the area of one trapezoidal lateral face. The area of a trapezoid is given by (1)/(2) (b_1 + b_2) h', where b_1 and b_2 are the parallel sides and h' is the height (which is the slant height l_f in this case). A_face = (1)/(2) (L_1 + L_2) l_f A_face = (1)/(2) (40 + 20) (10sqrt(37)) A_face = (1)/(2) (60) (10sqrt(37)) A_face = 30 × 10sqrt(37) = 300sqrt(37) cm^2 Step 4: Calculate the total lateral surface area (A_L). There are 4 identical lateral faces: A_L = 4 × A_face = 4 × 300sqrt(37) = 1200sqrt(37) cm^2 Step 5: Calculate the total surface area of the frustum. A_total = A_B + A_L A_total = 1600 + 1200sqrt(37) cm^2 The surface area of the frustum is 1600 + 1200sqrt(37) cm^2. c) The capacity of the frustum in litres Step 1: Calculate the area of the top and bottom