Question

The solid below is dilated by a scale factor of 1/4. Find the volume of the solid created upon dilation. Answer in terms of piπ. The numbers of the solid are 10 with 6 on the outside.

Answer 1

I don’t see the figure, so I’m not sure what kind of solid has the labels 10 and 6. But the method is the same: a dilation by scale factor k = 1/4 multiplies volume by k^3 = (1/4)^3 = 1/64. So compute the original volume, then divide by 64.

Here are the likely cases (using 10 and 6 as common dimension pairs):

- If it’s a cone with height 10 and base radius 6:
- Original V = (1/3)πr^2h = (1/3)π(6^2)(10) = 120π.
- After dilation V' = 120π ÷ 64 = 15/8 π.

- If it’s a cylinder with height 10 and radius 6:
- Original V = πr^2h = π(6^2)(10) = 360π.
- After dilation V' = 360π ÷ 64 = 45/8 π.

- If it were a sphere of radius 6:
- Original V = (4/3)π(6^3) = 288π.
- After dilation V' = 288π ÷ 64 = 9/2 π.

If you upload or describe the figure (what solid it is and which dimension is 10 and which is 6), I’ll give the single correct answer.