A bucket made up of a metal sheet is in the form of a frustum of cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively . Find the volume of the bucket . Also find the cost of the bucket if the cost of the metal used is Rs 20 per 100 cm².
Answers
Answer:
The total Cost of making the bucket is ₹ 391.87
Step-by-step explanation:
SOLUTION :
GIVEN :
Diameter of upper end of bucket = 40cm
Radius of the upper end of the frustum of cone( r1) = 40/2 = 20 cm
Diameter of lower end of bucket = 16 cm
radius of the lower end of the frustum of cone( r2) = 16/2 = 8 cm
Height of the frustum of Cone = 16 cm
Slant height of bucket ( L)= √(h² + (r1- r2)²
L =√16² + (20 - 8)² = √256 + 12²
L =√256+ 144
L = √400 = 20cm
L = 20 cm
Volume of bucket = π/3 (r1² + r2² + r1r2) h
= ⅓ × π (20² + 8² + 20×8)× 16
= ⅓ π (400 + 64 + 160)× 16
= ⅓ π × 624 × 16
= ⅓ × 3.14 × 624 × 16
= 3.14 × 208 × 16
= 10449.92 cm³
Volume of bucket = 10449.92 cm³
Surface area of metal sheet used in making a bucket = π(r1 + r2)L + πr2²
= 3.14(20 + 8) × 20 + π(8)²
= 3.14 × 28 × 20 + 64 × 3.14
= 3.14 (560+ 64)
= 624 × 3.14
= 1,959.36 cm²
Cost of making the bucket is = 1,959.36 cm² × 20/100
= 1,959.36 cm² × 0.2
= ₹ 391.87
Hence, the total Cost of making the bucket is ₹ ₹ 391.87
HOPE THIS ANSWER WILL HELP YOU....
Volume of bucket = 10449.92 cm ^3
Cost of metal used = Rs. 391.87