Question

A metallic bucket is in the shape of frustum of a cone.If the diameters of two circulear ends of the bucket are 45 and 25 cm respectively and total height is 24cm find the area of metallic sheet used to make the bucket.Also find the volume.

Answer 1

Answer:

Step-by-step explanation:

Given the frustum we can visualize two cones:

One smaller cone and one larger cone.

We need to get the the heights of the cone given the respective radii.

The Linear scale factor is given by :

radius of the cones :

Smaller cone = 25/2

Larger cone = 45/2

LSF = 45/2 ÷ 25/2 = 1.8

Let the height of the smaller cone be x.

The height of the larger cone will be :

Height = (x + 24) cm

Using the LSF we can get the value of x as follows:

1.8 = (x + 24)/x

1.8x = x + 24

1.8x - x = 24

0.8x = 24

x = 30 cm

The height of the larger cone is given by = 30 + 24 = 54 cm

We need the lateral height of the cones.

By pythagoras theorem the lateral heights of the cones is given by:

Smaller cone = √((25/2)² + 30²) = 32.5 cm

Larger cone = √((45/2)² + 54²) = 58.5 cm

Volume of the cones :

Smaller cone = 1/3 × 3.142 × (25/2)² × 30 = 4909.375 cm³

Larger cone = 1/3 × 3.142 × (45/2)² × 54 = 28631.475 cm³

Volume of the frustum = Volume of the larger cone - Volume of smaller cone

= 28631.475 - 4909.375 = 23722.1 cm³

Surface area of the cones is(Curved surface area) :

Small cone = 3.142 × 25 × 32.5 = 2552.875 cm²

Large cone = 3.142 × 45 × 58.5 = 8271.315 cm²

Curved surface area of the frustum = 8271.315 - 2552.875 = 5718.44 cm²

The area of the bottom of the frustum = 3.142 × (25/2)² = 490.9375 cm²

Total area of the bucket = 490.9375 + 5718.44 = 6209.3775 cm²