She bought it at a 15% discount because 15 percent of 40 is 6 and 40-6=34
Note that the interior angles must add up to 180 degrees: 50+62+m<C = 180.
Then 112 + m<C = 180, so that m<C =68 degrees.
Use the Law of Sines to find the value of a, as follows:
sin 50 deg sin 62 deg
-------------- = ----------------
a 31 cm
31sin 50 31(0.766)
Then 31sin 50 = a*sin 62, and a = --------------- = ---------------- = 26.9 cm
sin 62 0.883
a =
1. cylinder to cone:
(πr^2h)/((1/3)πr^2h) = 3:1
2. sphere to cylinder:
((4/3)πr^3)/(πr^2h) = 4r:3h
3. cone to sphere:
((1/3)πr^2h)/((4/3)πr^3) = h:4r
4. hemisphere to cylinder:
half the ratio of sphere to cylinder = 2r:3h
M= 6 so 2m would be 12 and 12-3=9
