The diameter of lower and the upper ends of a bucket is in the form of a frustum of a cone are 10cm and 30cm respectively if its height is 24cm then find,
(1)the area of the metal sheet used to make the bucket
(2) why we should avoid the bucket made of plastic?
(use \pi =3.14)
Answers
D=30 R=15
h=24
l=√h²+(R-r) ²
=√576+(10)²
=√576+100
=√676
=26
(i) Area of the metal sheet used:
=CSA of frustum +area of base of cylinder
=πl(R+r)+πr²
=π[l(R+r)+r²]
=3.14[26(15+5)+(5)²]
=3.14[26(20)+25]
=3.14[520+25]
=3.14[545]
=1711.30 cm²
(ii) Because plastic leads to water and soil pollution leading to severe consequences for environment along with increase in the spread of diseases and also deteriorate the quality of pure drinking water and soil.
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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
- Plastics are non-biodegradable and cause environmental pollution.
- Chemicals added to plastic are absorbed by human body.
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