A kitchenware company creates mixing bowls so that they fit inside of each other. The largest bowi has height of 64 cm and a diameter of 108 cm.
a) A bowl is made to fit inside of the largest bowl. It is created by dilating the largest howl using a scale factor of What is the height and diameter of the new smaller bowl? 4
b) Another bowl is created with a height of 9.28 cm and a diameter of 15.66 cm. What scale factor was applied in the dilation of the largest bowl to create this new bowl? Breakdown explain
a)
To find the height and diameter of the new smaller bowl, we need to use the scale factor of 4.
Height of new bowl = 64 cm / 4 = 16 cm
Diameter of new bowl = 108 cm / 4 = 27 cm
Therefore, the height of the new smaller bowl is 16 cm and the diameter is 27 cm.
b)
To find the scale factor applied in the dilation of the largest bowl to create the new bowl with a height of 9.28 cm and a diameter of 15.66 cm, we can use the formula:
Scale factor = Height of new bowl / Height of largest bowl = Diameter of new bowl / Diameter of largest bowl
Scale factor = 9.28 cm / 64 cm = 15.66 cm / 108 cm ≈ 0.145
Therefore, the scale factor applied in the dilation of the largest bowl to create the new smaller bowl is approximately 0.145.