Question

If the radii of the ends of a bucket are 5 cm and 15 cm and it is 24 cm high, then its surface area is ______.

Options

• 1815.3 cm²

•  1711.3 cm²

• 2025.3cm²

• 2360 cm²

Answer 1

If the radii of the ends of a bucket are 5 cm and 15 cm and it is 24 cm high, then its surface area is 1711.3 cm².

Explanation:

Let R and r be the radii of the top and base of the bucket, respectively, and let h and l be its height and slant height.

Then,  

R = 15 cm, r = 5 cm, h = cm

`l=sqrt("h"^2 + ("R" - r)^2)`

`=sqrt((24)^2 + (15 - 5)^2)`

`=sqrt(576+100)`

`=sqrt(676)`

= 26 cm

Surface area of the bucket` = pi["r"^2 + l("R" + "r")]`

`= 3.14xx(5^2 + 26(15+5))` 

`= (3.14xx(26xx20+25)) "cm"^2` 

`= 1711.3  "cm"^2`