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.