Question

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.

Answer 1

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.