Question

A metallic bucket, open at the top, of height 24 cm is in the form of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and 14 cm, respectively. Find

1. the volume of water which can completely fill the bucket;
2. the area of the metal sheet used to make the bucket.

Answer 1

We have,

Height, h = 24 cm,

Upper base radius, R = 14 cm and lower base radius, r = 7 cm

Also, the slant height, `l =sqrt(("R"-"r")^2 + "h"^2)`

`= sqrt((14-7)^2+24^2)`

`=sqrt(7^2+24^2)`

`=sqrt(49+576)`

`= sqrt(625)` 

= 25 cm

 i . Volume of the bucket`= 1/3 pi"h"("R"^2+"r"^2+"Rr")`

`= 1/3xx22/7xx24xx(14^2+7^2+14+7)`

`=22/7xx8xx(196+49+98)`

`=22/7xx343`

= 8624 cm³

So, the volume of water which can completely fill the bucket is 8624 cm³

ii . surface area of the bucket = π (R + r)l + πr² 

`=22/7xx(14+7)xx25+22/7xx7xx7`

`=22/7xx21xx25+22xx7`

= 22 × 3 × 25 + 22 × 7

= 1650 + 154

= 1804 cm²  

So, the area of the metal sheet used to make the bucket is 1804 cm² .