Question

A man donates 10 aluminium buckets to an orphanage . A bucket made of aluminium is of h=20cm and has its upper and lower end of r=36cm and 21 cm . Find the cost of preparing 10 buckets if the cost of aluminium is rs 42 per 100 cm sq

Answer 1

Formula to find the surface area of the bucket:

$\text {Surface Area = } \pi r^2 + \pi(R + r)\sqrt{(R - r)^2 + h^2}$

Find the surface area:

$\text {Surface Area = } \pi (21)^2 + \pi(36 + 21)\sqrt{(36 - 21)^2 + (20)^2}$

$\text {Surface Area = } 5864.57 \text{cm}^2$

Find the cost of 1 bucket:

$100 cm^2 = \text{Rs } 42$

$1cm^2 = \text{Rs } 0.42$

$5864.57 \text { cm}^2 = 5864.57 \times 0.42$

$15864.57 \text { cm}^2 = \text {Rs } 2463.12$

Find the cost of 10 buckets:

1 bucket = Rs 2463.12

10 buckets = 2463.12 x 10 = Rs 24,631.20

Answer: It costs Rs 24,631.20

Answer 2

since bucket is always in shape of frustum of cone thus
Area of 1 bucket=CSA of frustum +area of base
=πl(R+r)+πr×r
=π×25×57+π×441
=5859.24cm²
Area for 10 buckets=58592.4cm²
100cm²→42rupees
58592.4cm²→42/100×58592.4
=2460.8rupees