A bucket open at the top , and made up of a metal sheet is in the form of the frustum of a cone . The depth of bucket is 24cm and the diameter of its upper and lower circular ends are 30cm and 10cm respectively . Find the cost of metal sheet used in it at the rate of ₹10 per 100metre square.
[Use π =3.14]
Answers
diameter of uper end = 30cm
radius R = 30 ÷ 2 = 15cm
diameter of lower end = 10cm
radius = 10 ÷ 2 = 5cm
slant height l = √[( R - r)^2 + (h)^2]
l = √[ ( 15 - 5) + (24)^2 ]
l = √( 100 + 576) = √676
l = 26cm
surface are of Bucked that made of metal sheet
= π( R + r ) × l + πr^2
= 3.14 ( 15 + 5) × 26 +3.14(5)^2
= 1711.3cm^2
cost of 100cm^2 = ₹10
cost of 1cm^2 = 10 ÷ 100 = ₹0.1
cost of metal sheet used in it
= 0.1 × 1711.3
= ₹171.13
Answer: cost = ₹171.13
Answer:
171.3.
Step-by-step explanation:
Given, Depth of bucket h = 24 cm.
Let R and r be the radius of the upper and lower circular ends.
⇒ Radius of the upper end (R) = (30/2) = 15 cm.
⇒ Radius of the lower end (r) = (10/2) = 5 cm.
(i)
Let l be the slant height of the frustum, then
⇒ l = √h² + (R - r)²
= √(24)² + (15 - 5)²
= √576 + 100
= √676
= 26 cm.
(ii)
Total surface area of the bucket:
⇒ π(Rl + rl + r²)
⇒ (22/7) * (15 * 26 + 5 * 26 + 5²)
⇒ (22/7) * (545)
⇒ 1712.85 cm².
(iii)
Given that cost of 100 per m² = 10.
Then, the cost of metal sheet used = 1712.85 * (10/100)
= 1712.85 * 0.1
= 171.28
= 171.3(approx)
Therefore, the cost of metal sheet used to make the bucket = 171.3.
Hope it helps!