Question

a bucket open at the top is of the form of a frustum of a cone. The diameters of its upper and lower circular ends are 40cm and 20cm respectively. if total 17600 cu.cm of milk can be filled in the bucket, find its total surface area. what precautions should be taken for the bucket in which milk is kept?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The total surface area of the bucket is 2763.2 centimeter square.

Step-by-step explanation:

Given : A bucket open at the top is of the form of a frustum of a cone. The diameters of its upper and lower circular ends are 40cm and 20cm respectively. If total 17600 cu.cm of milk can be filled in the bucket.

To find : Its total surface area and what precautions should be taken for the bucket in which milk is kept?

Solution :

External diameter = 40 cm

External radius R= 20 cm

Internal diameter = 20 cm

Internal radius r= 10 cm

Height is h,

The volume of the bucket is V=17600 cu.cm

Formula of volume of the bucket is

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

$17600=\frac{1}{3}(3.14) h(10^2+(10)(20)+20^2)$

$17600=1.046 h(100+200+400)$

$17600=1.046 h(700)$

$h=\frac{17600}{1.046(700)}$

$h=24.03 cm$

The height of the bucket is approx 24 cm.

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

$l=\sqrt{24^2+(20-10)^2}$

$l=\sqrt{576+100}$

$l=\sqrt{676}$

$l=26$

Total surface area of the bucket is

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

$TSA=(3.14) [(20+10)26+10^2]$

$TSA=(3.14) [(30)26+100]$

$TSA=2763.2cm^2$

Therefore, The total surface area of the bucket is 2763.2 centimeter square.