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A wooden article was made by scooping out a hemisphere from each end of a solid cylinder as shown in the figure if the height of the cylinder is 12 cm and its base is of radius 4.2 cm find the total surface area of the article also find the volume of the wood left in the article?
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Given information:
- Height of the cylinder = 12 cm
- Radius of the base = 4.2 cm
Calculating the surface area of the wooden article:
To find the total surface area of the wooden article, we need to find the surface area of the cylinder and the two hemispheres.
1. Surface area of the cylinder:
The formula to calculate the surface area of a cylinder is given by:
Surface area of cylinder = 2πrh + 2πr^2
Given:
Height of the cylinder (h) = 12 cm
Radius of the base (r) = 4.2 cm
Substituting the values in the formula, we get:
Surface area of cylinder = 2π(4.2)(12) + 2π(4.2)^2
= 100.8π + 88.56π
= 189.36π cm^2
2. Surface area of the two hemispheres:
The formula to calculate the surface area of a hemisphere is given by:
Surface area of hemisphere = 2πr^2
Given:
Radius of the hemisphere (r) = 4.2 cm
Substituting the value in the formula, we get:
Surface area of hemisphere = 2π(4.2)^2
= 2π(17.64)
= 35.28π cm^2
Since there are two hemispheres, the total surface area of the hemispheres = 2 * 35.28π = 70.56π cm^2
Total surface area of the wooden article:
The total surface area of the wooden article is the sum of the surface area of the cylinder and the surface area of the two hemispheres.
Total surface area = Surface area of cylinder + Surface area of hemispheres
= 189.36π + 70.56π
= 259.92π cm^2
Therefore, the total surface area of the wooden article is 259.92π cm^2.
Calculating the volume of the wood left in the article:
To find the volume of the wood left in the article, we need to subtract the volume of the two hemispheres from the volume of the cylinder.
1. Volume of the cylinder:
The formula to calculate the volume of a cylinder is given by:
Volume of cylinder = πr^2h
Given:
Height of the cylinder (h) = 12 cm
Radius of the base (r) = 4.2 cm
Substituting the values in the formula, we get:
Volume of cylinder = π(4.2)^2(12)
= 705.6π cm^3
2. Volume of the two hemispheres:
The formula to calculate the volume of a hemisphere is given by:
Volume of hemisphere = (2/3)πr^3
Given:
Radius of the hemisphere (r) = 4.2 cm
Substituting the value in the formula, we get:
Volume of hemisphere = (2/3)π(4.2)^3
= (2/3)π(74.088)
= 98.784π cm^3
Since there are two hemispheres, the total volume of the
- Height of the cylinder = 12 cm
- Radius of the base = 4.2 cm
Calculating the surface area of the wooden article:
To find the total surface area of the wooden article, we need to find the surface area of the cylinder and the two hemispheres.
1. Surface area of the cylinder:
The formula to calculate the surface area of a cylinder is given by:
Surface area of cylinder = 2πrh + 2πr^2
Given:
Height of the cylinder (h) = 12 cm
Radius of the base (r) = 4.2 cm
Substituting the values in the formula, we get:
Surface area of cylinder = 2π(4.2)(12) + 2π(4.2)^2
= 100.8π + 88.56π
= 189.36π cm^2
2. Surface area of the two hemispheres:
The formula to calculate the surface area of a hemisphere is given by:
Surface area of hemisphere = 2πr^2
Given:
Radius of the hemisphere (r) = 4.2 cm
Substituting the value in the formula, we get:
Surface area of hemisphere = 2π(4.2)^2
= 2π(17.64)
= 35.28π cm^2
Since there are two hemispheres, the total surface area of the hemispheres = 2 * 35.28π = 70.56π cm^2
Total surface area of the wooden article:
The total surface area of the wooden article is the sum of the surface area of the cylinder and the surface area of the two hemispheres.
Total surface area = Surface area of cylinder + Surface area of hemispheres
= 189.36π + 70.56π
= 259.92π cm^2
Therefore, the total surface area of the wooden article is 259.92π cm^2.
Calculating the volume of the wood left in the article:
To find the volume of the wood left in the article, we need to subtract the volume of the two hemispheres from the volume of the cylinder.
1. Volume of the cylinder:
The formula to calculate the volume of a cylinder is given by:
Volume of cylinder = πr^2h
Given:
Height of the cylinder (h) = 12 cm
Radius of the base (r) = 4.2 cm
Substituting the values in the formula, we get:
Volume of cylinder = π(4.2)^2(12)
= 705.6π cm^3
2. Volume of the two hemispheres:
The formula to calculate the volume of a hemisphere is given by:
Volume of hemisphere = (2/3)πr^3
Given:
Radius of the hemisphere (r) = 4.2 cm
Substituting the value in the formula, we get:
Volume of hemisphere = (2/3)π(4.2)^3
= (2/3)π(74.088)
= 98.784π cm^3
Since there are two hemispheres, the total volume of the
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A wooden article was made by scooping out a hemisphere from each end of a solid cylinder as shown in the figure if the height of the cylinder is 12 cm and its base is of radius 4.2 cm find the total surface area of the article also find the volume of the wood left in the article?
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A wooden article was made by scooping out a hemisphere from each end of a solid cylinder as shown in the figure if the height of the cylinder is 12 cm and its base is of radius 4.2 cm find the total surface area of the article also find the volume of the wood left in the article? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A wooden article was made by scooping out a hemisphere from each end of a solid cylinder as shown in the figure if the height of the cylinder is 12 cm and its base is of radius 4.2 cm find the total surface area of the article also find the volume of the wood left in the article? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wooden article was made by scooping out a hemisphere from each end of a solid cylinder as shown in the figure if the height of the cylinder is 12 cm and its base is of radius 4.2 cm find the total surface area of the article also find the volume of the wood left in the article?.
A wooden article was made by scooping out a hemisphere from each end of a solid cylinder as shown in the figure if the height of the cylinder is 12 cm and its base is of radius 4.2 cm find the total surface area of the article also find the volume of the wood left in the article? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A wooden article was made by scooping out a hemisphere from each end of a solid cylinder as shown in the figure if the height of the cylinder is 12 cm and its base is of radius 4.2 cm find the total surface area of the article also find the volume of the wood left in the article? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A wooden article was made by scooping out a hemisphere from each end of a solid cylinder as shown in the figure if the height of the cylinder is 12 cm and its base is of radius 4.2 cm find the total surface area of the article also find the volume of the wood left in the article?.
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