Get personalized answers to your specific questions with IDNLearn.com. Discover in-depth answers to your questions from our community of experienced professionals.

The Volume, Vcm3, of a tin of radius r cm is given by the formula V=π (40r-r2-r3). Find the positive value or r for which dV/dr=0, and find the value of V which corresponds to this value of r.

Sagot :

[tex]V=\pi (40r-r^2-r^3) \\V=40\pi r-\pi r^2-\pi r^3 \\\\ \frac{dV}{dr}=40\pi -2\pi r-3\pi r^2 \\\\ \frac{dV}{dr}=0 \\40\pi -2\pi r-3\pi r^2=0 \\40-2r-3r^2 = 0 \\3r^2+2r-40 = 0 \\3r^2+12r-10r-40 = 0 \\3r(r+4)-10(r+4)=0 \\(3r-10)(r+4) \\r=-4,10/3[/tex]

r is positive, so r =10/3 cm

So, if r =10/3:

[tex]V=\pi (40r-r^2-r^3) \\V = \pi(40(10/3)-(10/3)^2-(10/3)^3) \\V=\pi(400/3-100/9-1000/27) \\V =\pi(85.185...) \\V = 85.185...\pi \\V = 267.617... \\V = 268 cm^3 (3 s.f.)[/tex]

Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find clear and concise answers at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.