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# solid mensuration

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The volume of the apple juice in a glass whose shape is an inverted frustum of a cone is 1176π mm³. The depth of the juice is 18mm.

Find the radius of the lower base if the product of its radii is 60 mm². *

a.5 mm

b.6 mm

c.7 mm

d.8mm

Jan 23, 2021

#1
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The volume of the apple juice in a glass whose shape is an inverted frustum of a cone is 1176π mm³. The depth of the juice is 18mm.

Find the radius of the lower base if the product of its radii is 60 mm². *

a.5 mm

b.6 mm

c.7 mm

d.8mm

Hello Guest!

$$V=\dfrac{1}{3}\pi h(R^2+Rr+r^2)\\ 1176mm^3=\dfrac{1}{3}\cdot 18mm\cdot (R^2+60mm^2+r^2)\\$$

$$Rr=60mm^2\\ R= \dfrac{60mm^2}{r}$$

$$1176mm^3=\dfrac{1}{3}\cdot 18mm\cdot ( (\frac{60mm^2}{r})^2+60mm^2+r^2)$$

$$(\frac{60mm^2}{r})^2+60mm^2+r^2=196mm^2\\ 3600mm^4+60r^2mm^2+r^4=196r^2mm^2\\ r^2=x$$

$$3600mm^4+60x\ mm^2+x^2=196x\ mm^2\\ 3600mm^4-136x\ mm^2+x^2=0$$

$$x=68\pm \sqrt{4624-3600}\\ x=68\pm 32\\ r=\sqrt{x}\\ r=\sqrt{68-32}$$

$$r=6\ mm$$

The radius of the base of the frustum of a cone is 6mm.

b. it's right.

!

Jan 23, 2021
edited by asinus  Jan 23, 2021
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