# 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. - Mathematics

Sum

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 cm

Also,

Total surface area of the bucket = πl (R + r) + πr

= 1/3xx22/7xx28xx(28^2+7^2+28xx7)

=88/3 xx (784+49+196)

= 88/3xx1029

= 30184 cm

Also,

Total surface area of the bucket  = πl(R + r)+πr

=22/7xx35xx(28+7)+22/7xx7xx7

=110xx(35)+154

= 3850 + 154

= 4004 cm

Disclaimer: The answer of the total surface area given in the textbook is incorrect. The same has been corrected above.

Is there an error in this question or solution?

#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 19 Volume and Surface Area of Solids
Exercise | Q 36 | Page 916