Geometry Worksheet

These problems deal as much with how certain words are used in mathematics and how these
words are changed into numbers or formulas . To make these more interesting I note had these are
exactly the type of surprise mystery question that I am likely to ask on the exam.

1. Recall the area A of a circle of radius r is A = πr².

(a) If the radius of a circle is increased from r = 1 by an amount Δr = .5 then

i. What is the new radius? (Don't try to make this hard.)
ii. What the the corresponding change ΔA in the area?
iii. What is the percent increase in the area?

(b) If the radius of a circle is decreased from r = 4 by an amount Δr = −1 ( we use the
negative sign to indicate decrease) then

i. What is the new radius?
ii. What the the corresponding change ΔA in the area?
iii. What is the percent decrease in the area?

(c) More generally if the radius r is changed by an amount Δr then

i. What is the new radius?
ii. What is the corresponding change in the area ?

(d) Is the radius of a circle is doubled , then by what factor does the area change by?
(e) Is a 20in pizza at three times the price of a 10in pizza a good deal?
(f) If the radius of a circle is doubled, then what is the percent change in the area ?
(g) If the area of a circle is doubled, then by what factor does the radius change?

2. The volume V of a right circular cylinder with base of radius r and height h is V = πr²h.

(a) If the radius of the of the cylinder is increased by 20% then what is the percent increase
in the volume?

(b) If the height of the cylinder is increased by 20% then what is the percent increase in the
volume?

(c) If the radius of the cylinder is doubled and the volume stays the same, then by what
factor does the height change?

(d) Which has the greater effect on the volume of the cylinder, doubling the radius or doubling
the height?

(e) What is the formula for the change ΔV in the volume of the cylinder when the radius is
changed by Δr and the height is changed by Δh? (This will involve some algebra .)