Question

what is the volume of sand in a bucket of base diameter 95cm, rim diameter 125 cm and height 100cm?

Answer 1

Answer:

Step-by-step explanation:

From the information given above the bucket is in form of a frustrum.

Let us make it a complete cone.

Let the height of the smaller cone be x.

The height of the bigger cone is:

(x + 100)

The linear scale factor is :

125/95 = 25/19

Now :

(x + 100)/x = 25/19

19(x + 100) = 25(x)

19x + 1900 = 25x

25x - 19x = 1900

6x = 1900

x = 1900/6

x = 316.67

The height of the bigger cone = 316.67 + 100 = 416.67

Volume of a cone = 1/3 × pie × r^2 × h

The larger cone :

Radius = 125/2 = 62.5

= 3.142 × 62.5 × 62.5 × 416.67 × 1/3

= 1704657.734

The smaller cone :

Radius = 47.5

= 3.142 × 47.5 × 47.5 × 316.67 × 1/3

= 748305.724

Volume of the frustrum is:

Volume of the frustrum = volume of larger cone - volume of smaller cone

1704657.734 - 748305.724 = 956352.01

= 956352.01 cubic centimeters.