Get expert advice and community support for all your questions on IDNLearn.com. Our experts provide timely and accurate responses to help you navigate any topic or issue with confidence.
Sagot :
From the information given, the volume of the sphere is approximately;
[tex]\begin{gathered} \text{Vol}=\frac{4}{3}\pi\times r^3 \\ \text{Vol}=\frac{4\times\pi\times2^3}{3} \\ \text{Vol}=\frac{32\pi}{3} \\ \text{Vol}\approx11\pi \end{gathered}[/tex]When Ricardo now places the two cones in the sphere, notice that the two cones each take up exactly one half of the entire sphere. However, the volume of either of them cannot be exactly the same as the volume of half the sphere. Also the two cones have taken up the entire cross section of the sphere, meaning that the height of each cone is congruent to the radius of the sphere.
Therefore, the volume of each cone is approximately;
[tex]\begin{gathered} \text{Vol}=\frac{1}{3}\pi\times r^2\times h \\ \text{Vol}=\frac{\pi\times2^2\times2}{3} \\ \text{Vol}=\frac{8\pi}{3} \\ \text{Volume of 2 cones would now be,} \\ 2\text{Vol}=\frac{2\times8\pi}{3} \\ 2\text{Vol}=\frac{16\pi}{3} \end{gathered}[/tex]Remember that the volume of the two cones is less than the volume of the entire sphere. That proves Ricardo's experiment as being correct that
[tex]\begin{gathered} \text{Volume of the sphere}<16\pi \\ \text{Volume of the sphere}>\frac{16\pi}{3} \end{gathered}[/tex](B) A good "estimate" (and not an exact answer) for the volume of the sphere would be to calculate the volume of the cylinder into which the sphere was placed. Observe that the sphere sits comfortably from top to bottom of the cylinder, which implies that, the entire cross section of the sphere (that is the diameter) equals the height of the cylinder.
Therefore, the cylinder would have,
[tex]\begin{gathered} \text{Radius}=2 \\ \text{Height}=4 \end{gathered}[/tex]
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Thank you for choosing IDNLearn.com for your queries. We’re committed to providing accurate answers, so visit us again soon.