Asked by Ian
The solid below is dilated by a scale factor of 1/2. Find the volume of the solid created upon dilation. Answer in terms of piπ. The line has a 4 and the side of the shape has a 9.
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Assuming the solid is a right circular cone with height 4 and slant height 9:
1. Find the radius: r = sqrt(9^2 − 4^2) = sqrt(81 − 16) = sqrt(65).
2. Original volume: V = (1/3)πr^2h = (1/3)π(65)(4) = (260/3)π.
3. After dilation by factor 1/2, volume scales by (1/2)^3 = 1/8: V_new = (260/3)π · 1/8 = (65/6)π.
Answer: (65/6)π.
1. Find the radius: r = sqrt(9^2 − 4^2) = sqrt(81 − 16) = sqrt(65).
2. Original volume: V = (1/3)πr^2h = (1/3)π(65)(4) = (260/3)π.
3. After dilation by factor 1/2, volume scales by (1/2)^3 = 1/8: V_new = (260/3)π · 1/8 = (65/6)π.
Answer: (65/6)π.
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