13. Area of cross-section A = 808.5 sq.cm. Inner
diameter d = 140 mm. Find out outer diameter D in
mm.
d
-D
A = 808.5 square cm
d = 140 mm
D =___mm?
Answers
Answer:
Using a bit of mental arithmetic to find the area of the circle of diameter “d” (and guessing, from your name, plus the diameter being a multiple of 7, that you’d use 22/7 as a close approximation for pi…)
The area of a circle can be calculated as πd²/4, which can be expressed as 22 x 140/7 x 140/4 (you can work out why I’ve done it that way) which in turn is 22 x 20 x 35, or 22 x 700, or 15,400mm² or 154 cm² look, no calculator…
It could have been done by converting the diameter to cm to start with, in which case
22 x 14/7 x 14/4 which still gets us 154 cm² even more quickly… Or using the radius (7cm)
22 x 7 x 7 / 7 = 154…even easier.
Add 154 to 808.5, getting 962.5. (962.5 is not a multiple of 7, but doubled, it is… confirming my suspicions that 22/7 ought to be used…) Quadrupled, it’s a multiple of 22, too, that’s surely no coincidence…
Anyway, πd²/4 = 962.5, πd² = 3,850, d² = 3,850 x 7 /22, d² = 175 x 7, d²= 1,225, and d = 35, so there’s your answer, using 22/7 for π, and no calculator. 22/7 is four ten thousandths greater than π, (0.0004.)
The fact that we arrived at a nice neat number really does confirm that the use of 22/7 was intended…
Getting the root of 1,225 without a calculator? Well, I know that 30² is 900, and suspected that the root of a number ending in 5 would itself end in 5, and that the root of 1,225 cannot be much greater than that of 900… So, I multiplied 35 x 35 on my scratch pad… As if by magic…
22/7 is great for non calculator problems. A circle’s area, given the diameter, is 22/28 x the diameter², or about 80% of the diameter² A circle’s diameter, given its area, is 28/22 x the square root of its area… A bit over 1.25 x the square root of the area. I mention these things, because they’re quick and dirty ways to establish if your answer is in the right ball park when you perform a calculation more formally…
Answer:
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