(3) A solid with surface area 8 square units is dilated by a scale factor of k to obtain a solid with surface area A square units. Find the value of k which leads to an image with each given surface area. PART A 512 square units PART B (1)/(2) square unit PART C 8 square units

Question

(3) A solid with surface area 8 square units is dilated by a scale factor of  k to obtain a solid with surface area  A square units. Find the value of  k which leads to an image with each given surface area. PART A 512 square units PART B  (1)/(2) square unit PART C 8 square units

Bytelearn · Accepted Answer

Calculate scale factor for PART A: Find the scale factor k for PART A where the surface area after dilation is 512 square units. Ratio of new surface area to original surface area = A / original surface area. Ratio = 512 / 8. Calculate the ratio. Ratio = 64. Since the ratio of the areas is the square of the scale factor, take the square root to find k. k = sqrt(64). Calculate k. k = 8.Calculate scale factor for PART B: Find the scale factor k for PART B where the surface area after dilation is (1)/(2) square units. Ratio of new surface area to original surface area = A / original surface area. Ratio = (1)/(2) / 8. Calculate the ratio. Ratio = (1)/(16). Since the ratio of the areas is the square of the scale factor, take the square root to find k. k = sqrt(1/16). Calculate k. k = 1/4.Calculate scale factor for PART C: Find the scale factor k for PART C where the surface area after dilation is 8 square units. Ratio of new surface area to original surface area = A / original surface area. Ratio = 8 / 8. Calculate the ratio. Ratio = 1. Since the ratio of the areas is the square of the scale factor, take the square root to find k. k = sqrt(1). Calculate k. k = 1.

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