the diameter of the lower and upper ends of a bucket in the form of a frustum of a cone are 10cm and 30 CM respectively if it's height is 24 CM. find
Answers
This question is incomplete. Total surface area of the metal sheet used to make the bucket is to be calculated in this question. I have solved a similar question.
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 cm
Total surface area of the metal sheet used = 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, total surface area of the metal sheet 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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