Question

A bucket is in the form of a frustum of a cone with a capacity of 12308.8 cm3
of water.
The radii of the top and bottom circular ends are 20cm and 12cm respectively. Find the
height of the bucket and the area of the metal sheet used in its making. (use π= 3.14)

Answer 1

Answer:

2342424

Step-by-step explanation:

Answer 2

Volume of the frustum is given by

V=

13πh(r12+r22+r1r2)

12308.8×3=πh(202+122+20×12)

12308.8×3=πh(400+144+240)

12308.8×3=πh(784)

12308×33.14×784=h

3920×3784=h

15cm = h

Hence, height of the frustum is 15 cm.

Now,

Metal sheet required to make the frustum = Curved surface area + Area of the base of the frustum

Curved surface area of the frustum =π(r1+r2)l, where l =

h2+(r1-r2)2

l=152+(20-12)2

=225+64

=289

=17 cm

Curved surface area of the frustum.

=π(20+12)17

=544×3.14

=1708.16 cm2

Area of the base =π122=144×3.14=452.16 cm2

∴ Metal sheet required to make the frustum=1708.16+452.16=2160.32 cm2