A bucket is in the form of a frustum of a cone and holds 15.25 litres of water. The diameters of the top and bottom are 25 cm and 20 cm respectively. Find its height and area of tin used in its construction.
Answers
Answer:
Height of the bucket (frustum of a cone) is 38.18 cm and Area of tin used in making the bucket (frustum of the cone) is 3017 cm² .
Step-by-step explanation:
SOLUTION :
Given :
Volume of bucket which is in the form of frustum of a cone= 15.25 litres = 15.25 × 1000 = 15250 cm³
[1 litres = 1000 cm³]
Diameter of bottom of bucket (Frustum of a cone) = 20 cm
Radius of bottom of bucket (Frustum of a cone), r = 20/2 = 10 cm
Diameter of top of bucket (Frustum of a cone) = 25 cm
Radius of top of bucket (Frustum of a cone), R = 25/2 = 12.5 cm
Volume of the bucket (frustum of a cone) = ⅓ πh(R² + r² + Rr)
15250 = ⅓ × π × h (12.5² + 10² + 12.5 × 10)
15250 = ⅓ ×22/7 ×h ( 156.25 + 100 + 125)
15250 × 3 × 7 = 22h × 381.25
h = (15250 × 3 × 7) / (22× 381.25)
h = 320,250 / 8,387.5
h = 38.18 cm
Height of the bucket (frustum of a cone) = 38.18 cm.
Slant height of the frustum, l = √h² + (R - r)²
l = √38.18² +(12.5 - 10)²
l = √1457.7124 + 2.5² = √1457.7124 + 6.25 = √1463.9624 = 38.26 cm
Slant height of the bucket, l = 38.26 cm
Area of tin used in making the bucket (frustum of the cone) = πl(R + r) + πr²
= π × 38.26 (12.5 + 10) + π × 10²
= π × 38.26 × 22.5 + 100 π
= π(38.26 × 22.5 + 100)
= π (860.85 + 100)
= 3.14 × 960.85
= 3017.06 = 3017 cm²
Area of tin used in making the bucket (frustum of the cone) = 3017 cm².
Hence, Height of the bucket (frustum of a cone) = 38.18 cm and Area of tin used in making the bucket (frustum of the cone) is 3017 cm² .
HOPE THIS ANSWER WILL HELP YOU….
Hence,
Height = 9.54 cm.
Now,
Area of Tin used in its Construction = C.S.A of Frustum + Area of Bottom Circle
Hence,
Area of Tin used in the Construction of the Container = 2,780. 14 cm^2
