a bucket made up of metal sheet is in the form of a frustum of a cone of height 16 - Maths - Surface Areas and Volumes

Question

a bucket made up of metal sheet is in the form of a frustum of a
cone of height 16 cm with radii of its lower and upper ends as 8 cm
and 20 cm respectively find the cost of the bucket if the cost of
the metal sheet is Rs 15 per 100 cm3 ( use pi= 22/7)

Lalit Mehra · Accepted Answer

Height of the bucket, h = 16 cm (Given)

Let the radii of the upper and lower ends of the bucket be r₁ and r₂respectively.

Given, r₁ = 20 cm and r₂ = 8 cm.

$Slant height of bucket, l = \sqrt{h^{2} + (r_{1} - r_{2})^{2}} = \sqrt{{(16 cm)}^{2} + (20 cm - 8 cm)^{2}} = \sqrt{{(16 cm)}^{2} + (12 cm)^{2}} = \sqrt{256 {cm}^{2} + 144 {cm}^{2}} = \sqrt{400 {cm}^{2}} = 20 cm$

Surface are of bucket

= Curved surface area of the bucket + Area of base of the bucket

= π(r₁ + r₂)l + πr₂²

= π [ (r₁ + r₂)l + r₂² ]

= $\frac{22}{7}$ [ (20 cm + 8 cm) 20 cm + (20 cm)² ]

= $\frac{22}{7}$ (28 × 20 cm² + 400 cm²)

= $\frac{22}{7}$ ( 560 cm² + 400 cm² )

= $\frac{22}{7}$ × 960 cm²

= 3017. 14 cm²(Approx)

Given, cost of 100 cm² metal sheet = Rs 15

$∴ C ost of the bucket = Rs \frac{15}{100} \times 3017.14 = Rs 452.60$ (Approx)

Thus, the cost of the bucket is approximately Rs 452.60.

a bucket made up of metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. find the cost of the bucket if the cost of the metal sheet is Rs. 15 per 100 cm3 ( use pi= 22/7)

a bucket made up of metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. find the cost of the bucket if the cost of the metal sheet is Rs. 15 per 100 cm³( use pi= 22/7)