A measuring glass is in the shape of an inverted conical vessel. It is found to be 8 cm deep and has a diameter of 3cm. What is the distance on the slant edge between the markings of the 1cc and 2cc.
Answers
Given : A measuring glass is in the shape of an inverted conical vessel. It is found to be 8 cm deep and has a diameter of 3cm. What is the distance on the slant edge between the markings of the 1cc and 2cc.
To Find : distance on the slant edge between the markings of the 1cc and 2cc.
Solution:
diameter = 3cm
radius = 1.5 cm
height = 8 cm
slant height = √8² + (3/2)² = √265 /2
Let say volume 1 cc is at x cm height
x/8 = r/1.5 = l/√265 /2
=> r= 3x/16 => l = √265x/16
slant height = √265x/16
Volume = (1/3)π(3x/16)²(x) = 1
=> x³ = 256/3π
=> x = 3.006
Let say volume 2 cc is at y cm height
y/8 = r/1.5
=> r= 3y/16
slant height = √265y/16
Volume = (1/3)π(3y/16)²(y) = 2
=> y³ = 512/3π
=> y = 3.787
distance on the slant edge between the markings of the 1cc and 2cc.
= √265y/16 - √265x/16
= (√265 / 16)(y - x)
= (√265 / 16)(3.787 - 3.006)
= 0.795
distance on the slant edge between the markings of the 1cc and 2cc. = 0.795 cm
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