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
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
(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
(g) If the area of a circle is doubled, then by what factor does the radius
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
in the volume?
(b) If the height of the cylinder is increased by 20% then what is the percent
increase in the
(c) If the radius of the cylinder is doubled and the volume stays the same, then
factor does the height change?
(d) Which has the greater effect on the volume of the cylinder, doubling the
radius or doubling
(e) What is the formula for the change ΔV in the volume of the cylinder when the
changed by Δr and the height is changed by Δh? (This will involve some algebra .)
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