Question

A bucket open at top in the form of frustum of a cone with capisity of 12308.8cm the radii of the top and bottom circular end are 20cm and 12cm respectively find the hight of the bucket and area of metal sheet used in making the bucket

Answer 1

check out the picture

Answer 2

Answer:

Step-by-step explanation:

here R=20 cm, r=12 cm

and volume is 12308.8 cm³

let the height of the bucket be h cm

the volume of bucket=volume of the frustum of the cone

1/3πh(R²+r²+Rr)=12308.8

=1/3×3.14×h[(20)²+(12)²+20×12]=12308.8

784h=12308.8×3/3.14

h=(12308.8×3/3.14×784)

h=15

the slant height of the bucket

l=√h²+(R-r)² units

l=√(15)²+(20-12)² cm

l=√(15)²+(8)²

l=√225+64

l=√289

l=17 cm

area of metal sheet used=(curved surface area)+(area of the bottom)

=[{πrl(R+r)}+πr²]

=[3.14×17×(20+12)+3.14×12×12]cm²

=[3.14×17×32+3.14×144]cm²

=[3.144×544+144]cm²

=[3.14×688]cm²

=2160.32cm²