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A cylinder and a cone have the same base and altitude. If the volume of the cone is 3030 cubic inches, what is the volume of the cylinder?\newlineA. 1010 cubic inches\newlineB. 1515 cubic inches\newlineC. 3030 cubic inches\newlineD. 6060 cubic inches\newlineE. 9090 cubic inches

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Q. A cylinder and a cone have the same base and altitude. If the volume of the cone is 3030 cubic inches, what is the volume of the cylinder?\newlineA. 1010 cubic inches\newlineB. 1515 cubic inches\newlineC. 3030 cubic inches\newlineD. 6060 cubic inches\newlineE. 9090 cubic inches
  1. Identify Formula: Identify the formula for the volume of a cone.\newlineVolume of a cone = (13)×base area×height(\frac{1}{3}) \times \text{base area} \times \text{height}
  2. Express Volume: Given that the volume of the cone is 3030 cubic inches, we can express this as:\newline30=13×base area×height30 = \frac{1}{3} \times \text{base area} \times \text{height}
  3. Calculate Cylinder Volume: To find the volume of the cylinder with the same base and altitude, we use the formula for the volume of a cylinder:\newlineVolume of a cylinder = base area ×\times height
  4. Deduce Volume Relationship: Since the base and height are the same for both the cone and the cylinder, we can deduce that the volume of the cylinder is three times the volume of the cone because the cone's volume is one third of the cylinder's volume.
  5. Calculate Cylinder Volume: Calculate the volume of the cylinder using the volume of the cone:\newlineVolume of the cylinder = 3×3 \times Volume of the cone\newlineVolume of the cylinder = 3×303 \times 30 cubic inches\newlineVolume of the cylinder = 9090 cubic inches

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