Question

100 POINTS!!!!

Two cylinders are similar with diameters 6 in and 9 in.
a. Find the ratio of the circumference of their bases


b. Find the ratio of the surface areas.



c. Find the ratio of the volumes.

Answer 1

• d=6in,9in
• r=3in,4.5in

circumference:-

`\\ \sf\longmapsto (2\pi r_1)/(2\pi r_2)`

`\\ \sf\longmapsto (6\pi)/(9\pi)`

`\\ \sf\longmapsto (2)/(3)`

`\\ \sf\longmapsto 2:3`

LSA:-

`\\ \sf\longmapsto (2\pi r_1h)/(2\pi r_2h)`

`\\ \sf\longmapsto (6)/(9)`

`\\ \sf\longmapsto (2)/(3)`

`\\ \sf\longmapsto 2:3`

TSA

`\\ \sf\longmapsto (2\pi r_1(h+r_1))/(2\pi r_2(h+r_2))`

`\\ \sf\longmapsto (6(h+6))/(9(h+9))`

`\\ \sf\longmapsto (6h+36)/(9h+81)`

`\\ \sf\longmapsto (h(6+36))/(h(9+81))`

`\\ \sf\longmapsto (42)/(90)`

`\\ \sf\longmapsto (7)/(15)`

`\\ \sf\longmapsto 7:15`

Volume:-

`\\ \sf\longmapsto (\pi r_1^2h)/(\pi r_2^2h)`

`\\ \sf\longmapsto (6^2)/(9^2)`

`\\ \sf\longmapsto (2)/(3)`

`\\ \sf\longmapsto 2:3`