Answer to Question #143156 in Geometry for preeti

Question #143156

 Amy measures the slant height of a cone-shaped cup and finds that it is 12 cm. The height is 10 cm. Determine the volume of water in the cup if Amy fills it to the top.


1
Expert's answer
2020-11-09T15:40:50-0500

Explanations & Calculations


  • If the radius of the base of the cone (the circle) is r, then considering a cross section of the cone through a diameter of the base circle, you can sense of a usage of Pythagoras theorem to find the radius (r) of the base.
  • Therefore,

r2+(10cm)2=(12cm)2r=122102=211cm\qquad\qquad \begin{aligned} \small r^2+(10cm)^2 &= \small (12cm)^2\\ \small r&= \small \sqrt{12^2-10^2}\\ &= \small \bold{2\sqrt{11} cm} \end{aligned}

  • And the volume of a cone is given is

V=13πr2h\qquad\qquad \begin{aligned} \small V &= \small \frac{1}{3}\pi r^2h\\ \small \end{aligned}

  • Therefore knowing both r & h, the volume is

V=13×π×(211cm)2×10cm=460.767cm3\qquad\qquad \begin{aligned} \small V&= \small \frac{1}{3}\times\pi \times(2\sqrt{11}cm)^2\times10cm\\ \small &= \small \bold{460.767cm^3} \end{aligned}


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