Sheet Capacity

. A sheet of metal in the form of a sector of a circle of 90 degrees and 16 cm radio remains?

. A sheet of metal in the form of a sector of a circle angle of 90 degrees and 16 cm radius bends to form a conical cup open. The capacity of the cup is A) 64 sqrt (15) cm3 B) 64 sqrt (3.5) TTcm3 C) 64 sqrt (5) TT D) 64/3sqrt (15) cm3 E) None of these

A sheet of metal in the form of a sector of a circle of 90 degrees and the radius of 16 cm folded to form a conical cup open. After retiring, the base of the cone is a circle whose circumference is equal to the length of the arc of the sector. It 32.pi / 4 = 8 cm pi. Therefore, the base circle radius is 8 pi / 2 pi = 4 cm. ——- (The base diameter is 8 cm) h (cone height) Note: the hypotenuse 16 ^ 2 = 4 ^ ^ 2 + 2 h, which h = 4 ^ 2 (4 ^ 2 – 1) = 15 * 4 ^ 2, so that h = 4 sqrt (15) Therefore, the volume of the cone (1 / 3 Base area * Height ) ^ = 1 / 3 pi r 2 h = 1 / 3 pi ^ 2 4 4 * sqrt (15) = 64 / 3 sqrt (15) cm ^ 3 Answer: The capacity of the cup is D) 64/3sqrt (15) cm3

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