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An ice cream seller has two types of ice cream container in the form of cylindrical shape and a cone with hemi-spherical base. Both have same height of 7 cm and same diameter of 7 cm. The cost of container are same but the seller decide to sell ice cream in cylindrical containers. (i) Calculate the volume of the both containers. (ii) Which value is depicted by the seller?
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An ice cream seller has two types of ice cream container in the form o...
Volume=449.1value depicted is that he was honest and wanted child's to take more ice cream
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An ice cream seller has two types of ice cream container in the form o...
Volume Calculation:
To calculate the volume of the cylindrical container, we can use the formula:
V_cylinder = π * r^2 * h
where π is a mathematical constant approximately equal to 3.14, r is the radius of the base, and h is the height of the container. In this case, the diameter is given as 7 cm, so the radius (r) would be half of that, which is 3.5 cm.
Substituting the values into the formula, we get:
V_cylinder = 3.14 * (3.5 cm)^2 * 7 cm
= 3.14 * 12.25 cm^2 * 7 cm
= 269.5 cm^3
Therefore, the volume of the cylindrical container is 269.5 cm^3.
To calculate the volume of the cone with a hemispherical base, we need to find the volume of the cone and the volume of the hemisphere separately, and then add them together.
The volume of the cone can be calculated using the formula:
V_cone = (1/3) * π * r^2 * h
where r is the radius of the base and h is the height of the cone. In this case, the radius is 3.5 cm, and the height is 7 cm.
Substituting the values into the formula, we get:
V_cone = (1/3) * 3.14 * (3.5 cm)^2 * 7 cm
= 3.14 * 12.25 cm^2 * 7 cm / 3
= 76.97 cm^3
The volume of the hemisphere can be calculated using the formula:
V_hemisphere = (2/3) * π * r^3
where r is the radius of the hemisphere. In this case, the radius is 3.5 cm.
Substituting the values into the formula, we get:
V_hemisphere = (2/3) * 3.14 * (3.5 cm)^3
= 2 * 3.14 * 42.875 cm^3 / 3
= 179.67 cm^3
Adding the volume of the cone and the volume of the hemisphere, we get:
V_cone_hemisphere = V_cone + V_hemisphere
= 76.97 cm^3 + 179.67 cm^3
= 256.64 cm^3
Therefore, the volume of the cone with a hemispherical base is 256.64 cm^3.
Depicted Value:
The seller's decision to sell ice cream in cylindrical containers instead of the more voluminous cone with a hemispherical base depicts the value of profit maximization. By choosing the cylindrical containers, the seller is able to utilize the space more efficiently and fit more ice cream in the same volume compared to the cone. This allows the seller to potentially sell more ice cream and increase their profits.
The cylindrical shape has a greater volume (269.5 cm^3) compared to the cone with a hemispherical base (256.64 cm^3) despite having the same height and diameter. This means that more ice cream can be accommodated in the cylindrical containers, providing more value to the customers
To calculate the volume of the cylindrical container, we can use the formula:
V_cylinder = π * r^2 * h
where π is a mathematical constant approximately equal to 3.14, r is the radius of the base, and h is the height of the container. In this case, the diameter is given as 7 cm, so the radius (r) would be half of that, which is 3.5 cm.
Substituting the values into the formula, we get:
V_cylinder = 3.14 * (3.5 cm)^2 * 7 cm
= 3.14 * 12.25 cm^2 * 7 cm
= 269.5 cm^3
Therefore, the volume of the cylindrical container is 269.5 cm^3.
To calculate the volume of the cone with a hemispherical base, we need to find the volume of the cone and the volume of the hemisphere separately, and then add them together.
The volume of the cone can be calculated using the formula:
V_cone = (1/3) * π * r^2 * h
where r is the radius of the base and h is the height of the cone. In this case, the radius is 3.5 cm, and the height is 7 cm.
Substituting the values into the formula, we get:
V_cone = (1/3) * 3.14 * (3.5 cm)^2 * 7 cm
= 3.14 * 12.25 cm^2 * 7 cm / 3
= 76.97 cm^3
The volume of the hemisphere can be calculated using the formula:
V_hemisphere = (2/3) * π * r^3
where r is the radius of the hemisphere. In this case, the radius is 3.5 cm.
Substituting the values into the formula, we get:
V_hemisphere = (2/3) * 3.14 * (3.5 cm)^3
= 2 * 3.14 * 42.875 cm^3 / 3
= 179.67 cm^3
Adding the volume of the cone and the volume of the hemisphere, we get:
V_cone_hemisphere = V_cone + V_hemisphere
= 76.97 cm^3 + 179.67 cm^3
= 256.64 cm^3
Therefore, the volume of the cone with a hemispherical base is 256.64 cm^3.
Depicted Value:
The seller's decision to sell ice cream in cylindrical containers instead of the more voluminous cone with a hemispherical base depicts the value of profit maximization. By choosing the cylindrical containers, the seller is able to utilize the space more efficiently and fit more ice cream in the same volume compared to the cone. This allows the seller to potentially sell more ice cream and increase their profits.
The cylindrical shape has a greater volume (269.5 cm^3) compared to the cone with a hemispherical base (256.64 cm^3) despite having the same height and diameter. This means that more ice cream can be accommodated in the cylindrical containers, providing more value to the customers
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An ice cream seller has two types of ice cream container in the form of cylindrical shape and a cone with hemi-spherical base. Both have same height of 7 cm and same diameter of 7 cm. The cost of container are same but the seller decide to sell ice cream in cylindrical containers. (i) Calculate the volume of the both containers. (ii) Which value is depicted by the seller?
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An ice cream seller has two types of ice cream container in the form of cylindrical shape and a cone with hemi-spherical base. Both have same height of 7 cm and same diameter of 7 cm. The cost of container are same but the seller decide to sell ice cream in cylindrical containers. (i) Calculate the volume of the both containers. (ii) Which value is depicted by the seller? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An ice cream seller has two types of ice cream container in the form of cylindrical shape and a cone with hemi-spherical base. Both have same height of 7 cm and same diameter of 7 cm. The cost of container are same but the seller decide to sell ice cream in cylindrical containers. (i) Calculate the volume of the both containers. (ii) Which value is depicted by the seller? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ice cream seller has two types of ice cream container in the form of cylindrical shape and a cone with hemi-spherical base. Both have same height of 7 cm and same diameter of 7 cm. The cost of container are same but the seller decide to sell ice cream in cylindrical containers. (i) Calculate the volume of the both containers. (ii) Which value is depicted by the seller?.
An ice cream seller has two types of ice cream container in the form of cylindrical shape and a cone with hemi-spherical base. Both have same height of 7 cm and same diameter of 7 cm. The cost of container are same but the seller decide to sell ice cream in cylindrical containers. (i) Calculate the volume of the both containers. (ii) Which value is depicted by the seller? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about An ice cream seller has two types of ice cream container in the form of cylindrical shape and a cone with hemi-spherical base. Both have same height of 7 cm and same diameter of 7 cm. The cost of container are same but the seller decide to sell ice cream in cylindrical containers. (i) Calculate the volume of the both containers. (ii) Which value is depicted by the seller? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An ice cream seller has two types of ice cream container in the form of cylindrical shape and a cone with hemi-spherical base. Both have same height of 7 cm and same diameter of 7 cm. The cost of container are same but the seller decide to sell ice cream in cylindrical containers. (i) Calculate the volume of the both containers. (ii) Which value is depicted by the seller?.
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An ice cream seller has two types of ice cream container in the form of cylindrical shape and a cone with hemi-spherical base. Both have same height of 7 cm and same diameter of 7 cm. The cost of container are same but the seller decide to sell ice cream in cylindrical containers. (i) Calculate the volume of the both containers. (ii) Which value is depicted by the seller?, a detailed solution for An ice cream seller has two types of ice cream container in the form of cylindrical shape and a cone with hemi-spherical base. Both have same height of 7 cm and same diameter of 7 cm. The cost of container are same but the seller decide to sell ice cream in cylindrical containers. (i) Calculate the volume of the both containers. (ii) Which value is depicted by the seller? has been provided alongside types of An ice cream seller has two types of ice cream container in the form of cylindrical shape and a cone with hemi-spherical base. Both have same height of 7 cm and same diameter of 7 cm. The cost of container are same but the seller decide to sell ice cream in cylindrical containers. (i) Calculate the volume of the both containers. (ii) Which value is depicted by the seller? theory, EduRev gives you an
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