Question

a bucket open at the top in the form of frustum of a cone with the capacity of 1208.8 centimeter cube the radii of top and bottom as circular x 20 cm and 12 cm respectively find the height of bucket area of matelled sheet used in making the bucket

Answer 1

check out the picture

Answer 2

Answer:

The area of metlled sheet used in bucket is 2160.32 cm square.

Step-by-step explanation:

Given : A bucket open at the top in the form of frustum of a cone with the capacity of 1208.8 centimeter cube the radii of top and bottom as circular 20 cm and 12 cm respectively.

To find : The height of bucket area of metelled sheet used in making the bucket?

Solution :

Volume of the frustum V=1208.8 cm cube.

Radius of the top R=20 cm.

radius of the bottom r=12 cm.

The volume of the frustum is

$V=\frac{1}{3}\pi (R^2+r^2+rR)h$

$1208.8=\frac{1}{3}\times 3.14\times(20^2+12^2+(20)(12))h$

$h=\frac{1208.8\times 3}{3.14\times(400+144+120)}$

$h=\frac{1208.8\times3}{3.14\times664}$

$h=15$

The height of the frustum is h=15 cm.

The slant height of the frustum is

$l=\sqrt{h^2+(R-r)^2}$

$l=\sqrt{15^2+(20-12)^2}$

$l=\sqrt{225+64}$

$l=\sqrt{289}$

$l=17$

The slant height is l=17 cm.

Total area of metal sheet used = CSA+ Base Area

$TSA=\pi (R+r)l+\pi r^2$

$TSA=3.14\times (20+12)\times 17+3.14\times 12\times 12$

$TSA=1708.16+452.16$

$TSA=2160.32$

Therefore, The area of metlled sheet used in bucket is 2160.32 cm square.