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A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone at the other end. Their common diameter is 4.2 cm and the heights of the cylindrical and conical portions are 12 cm and 7 cm respectively. The approximate volume of the toy will be
- a)250 cm3
- b)200 cm3
- c)300 cm3
- d)218 cm3
Correct answer is option 'D'. Can you explain this answer?
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To find the volume of the toy, we need to find the volumes of the cylindrical, hemispherical, and conical parts separately and then add them together.
1. Volume of the Cylinder:
The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. Since the diameter is given as 4.2 cm, the radius (r) is half of that, which is 2.1 cm. The height (h) is given as 12 cm. Substituting these values into the formula, we get:
Vcylinder = π(2.1 cm)²(12 cm)
Vcylinder ≈ 166.32 cm³
2. Volume of the Hemisphere:
The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius. Since the diameter is given as 4.2 cm, the radius (r) is half of that, which is 2.1 cm. Substituting this value into the formula, we get:
Vhemisphere = (2/3)π(2.1 cm)³
Vhemisphere ≈ 24.572 cm³
3. Volume of the Cone:
The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius and h is the height. Since the diameter is given as 4.2 cm, the radius (r) is half of that, which is 2.1 cm. The height (h) is given as 7 cm. Substituting these values into the formula, we get:
Vcone = (1/3)π(2.1 cm)²(7 cm)
Vcone ≈ 10.972 cm³
4. Total Volume:
To find the total volume of the toy, we add the volumes of the cylindrical, hemispherical, and conical parts together:
Vtotal = Vcylinder + Vhemisphere + Vcone
Vtotal ≈ 166.32 cm³ + 24.572 cm³ + 10.972 cm³
Vtotal ≈ 201.864 cm³
Since the volume of the toy is approximately 201.864 cm³, the closest option is 218 cm³ (option D).
1. Volume of the Cylinder:
The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. Since the diameter is given as 4.2 cm, the radius (r) is half of that, which is 2.1 cm. The height (h) is given as 12 cm. Substituting these values into the formula, we get:
Vcylinder = π(2.1 cm)²(12 cm)
Vcylinder ≈ 166.32 cm³
2. Volume of the Hemisphere:
The formula for the volume of a hemisphere is V = (2/3)πr³, where r is the radius. Since the diameter is given as 4.2 cm, the radius (r) is half of that, which is 2.1 cm. Substituting this value into the formula, we get:
Vhemisphere = (2/3)π(2.1 cm)³
Vhemisphere ≈ 24.572 cm³
3. Volume of the Cone:
The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius and h is the height. Since the diameter is given as 4.2 cm, the radius (r) is half of that, which is 2.1 cm. The height (h) is given as 7 cm. Substituting these values into the formula, we get:
Vcone = (1/3)π(2.1 cm)²(7 cm)
Vcone ≈ 10.972 cm³
4. Total Volume:
To find the total volume of the toy, we add the volumes of the cylindrical, hemispherical, and conical parts together:
Vtotal = Vcylinder + Vhemisphere + Vcone
Vtotal ≈ 166.32 cm³ + 24.572 cm³ + 10.972 cm³
Vtotal ≈ 201.864 cm³
Since the volume of the toy is approximately 201.864 cm³, the closest option is 218 cm³ (option D).
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A solid toy is in the form of a right circular cylinder with a hemispherical shape at one end and a cone at the other end. Their common diameter is 4.2 cm and the heights of the cylindrical and conical portions are 12 cm and 7 cm respectively. The approximate volume of the toy will bea)250 cm3b)200 cm3c)300 cm3d)218 cm3Correct answer is option 'D'. Can you explain this answer?
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