A bucket has top and bottom diameters of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm².(use π=3.14)
Answers
Step-by-step explanation:
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Cost of tin sheet of the bucket = Rs. 214.44
Step-by-step explanation:
Bottom radius r = 20/2 = 10cm
Top radius R = 40/2 = 20cm
Height of bucket h = 12cm
Volume of the bucket = 1/3πh(R² + r² +Rr)
= 1/3 * 22/7 * 12 (20² + 10² + 200)
= 22/7 * 4 (700)
= 8800 cu.cm.
Slant height of frustum l = root of (h² + (R-r)²) = root (12² + (20-10)²)
= root (144 + 100)
= 15.62 cm
Curved Surface area of bucket = π(R+r)l = 22/7 * 30 * 15.62 = 1472.74 sq.cm.
Area of base = πr² = 22/7 * 10 * 10 = 314.29 sq.cm.
Total surface area of the metal sheet = 1472.74 + 314.29 = 1787.03 sq.cm.
Cost of one dm² of metal sheet = Rs. 1.20
Cost of one cm² of metal sheet = Rs. 0.12
Therefore cost of tin sheet of the bucket = 0.12 * 1787.03 = Rs. 214.44