find the area of the metal sheet used to make the bucket when the diameterof the lower and upper ends of abucket in the form of the frustum of a cone are 10cm and 30cm respectively if its height is 24cm.
Answers
Diameter of the upper end = 30 cm
Radius r1 = 30/2 = 15 cm
Diameter of the lower end = 10 cm
Radius = r2 = 10/2 = 5 cm
Height = 24 cm
Slant Height 'l' = √h² + (r1 - r2)²
⇒ √24² + (15 - 5)²
⇒ √576 + (10)²
⇒ √576 + 100
⇒ √676
l = 26
So, slant height is 26 cm
Total surface area of the metal sheet = π(r1 + r2)l + πr2²
⇒ 22/7*(15 + 5)*26 + 22/7*5*5
⇒ (22*20*26)/7 + (22*25)/7
⇒ 11440/7 + 550/7
⇒ 1634.28 cm² + 78.57 cm²
= 1712.85 cm²
So, area of the metal used to make the bucket is 1712.85 cm².
Answer.
Given:
Diameter of the upper end = 30 cm
Diameter of the lower end = 10 cm
Height = 24 cm
To find:
Area
Solution:
Radius of the upper end of the cone = 15 cm
Radius of the lower end of the cone = 5 cm
In order to find the area,
The slant height should be calculated.
Slant height = √ ( h^2 + ( Radius of the upper end of the cone - Radius of the lower end of the cone )^2
√24^2 + ( 15 - 5 )^2
√576 + 10^2
Slant height = 26 cm
Area of the metal = Curved surface Area + Area of base of the cone.
Curved surface area = π ( Radius of the upper end of the cone - Radius of the lower end of the cone ) * Slant height
Area of the base = πr2^2
Hence,
π ( Radius of the upper end of the cone - Radius of the lower end of the cone ) * Slant height + πr2^2
3.14 ( 15 + 5 ) × 26 + π( 5 )^2
3.14 × 20 × 26 + 25 × 3.14
545 × 3.14
Area = 1711.3 sq.cm
Hence, the area of metal sheet used to make the bucket is 1711.3 sq.cm
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