If the radii of the circular ends of a bucket 28 cm high, are 28 cm and 7 cm, then find its capacity and total surface area.
Solution
We have,
Height, h = 28 cm
Radius of the upper end, R = 28 cm and
Radius of the lower end r = 7 cm,
Also,
The slant height, `"l" = sqrt(("R" - r)^2 + "h"^2)`
`=sqrt((28 - 7)^2+28^2)`
`=sqrt(21^2 + 28^2)`
`=sqrt(441 + 784)`
`=sqrt(1225)`
= 35 cm
Now,
capacity of the bucket`= 1/3pi"h" ("R"^2 + "r"^2+"Rr")`
`= 1/3xx22/7xx28xx(28^2+7^2+"Rr")`
`=88/3 xx (784+49+196)`
`= 88/3xx1029`
= 30184 cm3
Also,
Total surface area of the bucket = πl (R + r) + πr2
`= 1/3xx22/7xx28xx(28^2+7^2+28xx7)`
`=88/3 xx (784+49+196)`
`= 88/3xx1029`
= 30184 cm3
Also,
Total surface area of the bucket = πl(R + r)+πr2
`=22/7xx35xx(28+7)+22/7xx7xx7`
`=110xx(35)+154`
= 3850 + 154
= 4004 cm2
Disclaimer: The answer of the total surface area given in the textbook is incorrect. The same has been corrected above.
