Show the steps clearly.
1. OPQR is a sector of a circle with centre O. If arc PQ: arc QR = 5:4. Angle POR = 2x and angle PQR = 4x, find angle PRQ.
2. A solid consisting of a right circular cone and a semi-sphere of same radius 3cm. If the height of the solid is h cm and its volume is 33 pie cm^3, find h.
Urgent question3
2009-03-14 12:40 am
回答 (1)
2009-03-14 1:02 am
✔ 最佳答案
(360 - 2x)/2 = 4x ( angle at circumference is half angle at centre)360 - 2x = 8x
x = 360/10 = 36.
So 2x = 72.
Angle QOP = (72)[5/(5 + 4)] = (72)(5/9) = 40.
so angle PRQ = 40/2 = 20. ( Angle at circumference is half angle at centre).
2.
Volume of hemisphere = 2p(3)^3/3 = 18p ( p = pi).
Height of cone = h - 3
so volume of cone = p(3)^2(h - 3)/3 = 3p(h - 3).
so 18p + 3p(h -3) = 33p
18 + 3h - 9 = 33
3h = 33 + 9 = 42
h = 42/3 = 14.
收錄日期: 2021-04-25 22:39:18
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