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MTH 250 Graded Assignment 10, part one Area of plane figures Q1: Semicircles are placed on the sides of an equilateral triangle with side length 5.78 ft as shown below. Find the shaded area of the figure. Q2: Find the area of the triangle ABC shown in the figure below ( AB 45, BC 61, AC 98 ; figure not drawn to scale) in two ways: a) By using the Pythagorean Theorem to compute x and h, and the area formula A b) By using Heron's Formula. 1 bh . 2 Q3: Use the axioms for area (and any previously proven results) to prove the formula K 1 b1 b2 h for the area of a trapezoid having bases of length b1 and b2 and height h . 2 [Kay, section 4.6, page 295, #6(b)] Volume and surface area of solids Q4: Find the volume and surface area of a closed hemisphere with radius 3.5cm. Note you'll, have to modify the formulas, particularly the SA one – the half-sphere has a flat circular top. Q5: Find the ratio of the volume to the cylinder to the volume of the hemisphere, given that the height h of the cylinder is equal to the diameter d of the hemisphere. Q6: The volume of a square pyramid is 324 cubic feet. Find the value of x (length of side of square base). Then find the surface area of the pyramid.