A bucket open at the top, and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24 cm and the diameters of its upper and lower circular ends are 30 cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of Rs. 10 per 100 cm². (Use π = 3.14).
Answers
Answer:
The cost of metal sheet used is ₹ 171.13.
Step-by-step explanation:
SOLUTION :
GIVEN :
Diameter of upper circular end of a bucket = 30 cm
Radius of the upper end of the bucket , R = 30/2 = 15 cm
Diameter of lower circular end of a bucket = 10 cm
Radius of the lower end of the bucket , R = 10/2 = 5 cm
Height of the bucket, h = 24 cm
Slant height of a bucket , l = √(R - r)² + h²
l =√(15 - 5)² + 24²
l = √10² + 576
l = √100 + 576
l = √676
l = 26 cm
Slant height of a bucket ,l = 26 cm
Surface area of the bucket = Curved surface area of a bucket + Area of the smaller circular base
= π(R+ r)l + πr²
= π(15 + 5) × 26 + π× 5²
= π(20 × 26 + 25)
= π(520 + 25)
= π × 545
= 3.14 × 545
= 1711.3 cm²
Surface area of the bucket = 1711.3 cm²
cost of metal sheet used @ of ₹10 per 100 cm² = 1711.3 cm² × 10/100
= 1711.3 × 0.1 = ₹ 171.13
Hence, cost of metal sheet used is ₹ 171.13.
HOPE THIS ANSWER WILL HELP YOU…..
Answer:
Diameter of upper end of bucket = 30cm
Diameter of lower end of bucket = 10cm
Then, radius of upper end of bucket r
1
=
2
30
=15 cm
And, radius of lower end of bucket r
2
=
2
10
=5 cm
Height of bucket = 24 cm
Slant height of bucket =
(r
2
−r
1
)
2
+h
2
=
(15−5)
2
+(24)
2
=
(10)
2
+(24)
2
=
100+256
=
676
=26 cm
Area of metal sheet used to make bucket
=π(r
1
+r
2
)l+π(r
2
)
2
=π(15+5)26+π(5)
2
=520π+25π=545π cm
2
Given cost of 100 sq cm metal sheet =Rs.10
Cost of 545π cm
2
metal sheet =
100
545×3.14×10
=171.13 Rs.
Cost of metal sheet used for making bucket = Rs.171.13