The area of the base of a cone is 1386 cm² and the height of the cone is 54…
2021
The area of the base of a cone is 1386 cm² and the height of the cone is 54 cm. If the cone is melted to form solid hemispheres of radius 3 cm, then how many hemispheres will be formed?
- A.
664
- B.
332
- C.
882
- D.
441
Attempted by 3 students.
Show answer & explanation
Correct answer: D
To determine how many hemispheres can be formed, we must calculate the volume of the cone and the volume of a single hemisphere, then divide the cone's volume by the hemisphere's volume.
Step-by-Step Solution
Calculate the volume of the cone:
The formula for the volume of a cone is (1/3) * Base Area * Height.
Base Area = 1386 cm²
Height = 54 cm
Volume of cone = (1/3) * 1386 * 54
Volume of cone = 1386 * 18 = 24948 cm³
Calculate the volume of one hemisphere:
The formula for the volume of a hemisphere is (2/3) * π * r³, where r = 3 cm.
Volume of hemisphere = (2/3) * (22/7) * (3 * 3 * 3)
Volume of hemisphere = (2/3) * (22/7) * 27
Volume of hemisphere = 2 * (22/7) * 9
Volume of hemisphere = 396 / 7 cm³ ≈ 56.57 cm³
Determine the number of hemispheres:
Number of hemispheres = Volume of cone / Volume of one hemisphere
Number of hemispheres = 24948 / (396 / 7)
Number of hemispheres = 24948 * (7 / 396)
Number of hemispheres = 63 * 7 = 441
The total number of hemispheres formed is 441.