Question

A triangle with area 10 cm2 is dilated by a factor of 2.
What is the area of the dilated image?

_________ cm2

a pyramid with the volume of 1000 ft^3 is dilated by a factor of 1.5.
What is the volume of the scaled image?

A cylinder with the volume 22.8 mm^3 is dilated so that its new volume is 615.6mm^3.
By what factor was the cylinder dilated?

Answer 1

Triangle: 10cm² x 2² = 10cm² x 4 = 40 cm²
Since the area has an exponent of two. The factor should also be raised to the 2nd power to get the area of the dilated image.

Pyramid: 1000ft³ x 1.5³ = 1000ft³ x 3.375 = 3,375ft³
Volume has an exponent of 3. Thus, factor should be raised to the 3rd power to get the volume of the scaled image.

Cylinder: 615.60mm³ ÷ 22.80mm³ = 27
               dilation of the cylinder: ∛27 = 3
Volume has an exponent of 3. We need to get the cube root of the factor used to dilate the cylinder.