A circle with a radius of 1/2ft is dilated by a scale factor of 8. Which statements about the new circle are true? Check all that apply. The length of the new radius will be 4 feet. The length of the new radius will be 32 feet. The new circumference will be 8 times the original circumference. The new circumference will be 64 times the original circumference. The new area will be 8 times the original area. The new area will be 64 times the original area. The new circumference will be feet. The new area will be square feet.

Answer:A) The length of the new radius will be 4 feet C) The new circumference will be 8 times the original circumferenceF) The new area will be 64 times the original areaH) The new area will be 16π square feetStep-by-step explanation:Verify each statementsee the attached figure to better understand the problemPart A) The length of the new radius will be 4 feet The statement is trueBecausewe know thatThe radius of the original circle is r=1/2 ftThe scale factor is 8soTo find out the length of the new radius multiply the radius of the original circle by the scale factor(1/2)(8)=4 ftPart B)  The length of the new radius will be 32 feet.The statement is falseBecause, the length of the new radius is 4 ft (see part A)Part C) The new circumference will be 8 times the original circumferenceThe statement is trueBecauseThe original circumference is equal to[tex]C=\pi (\frac{1}{2})[/tex][tex]C=\frac{1}{2}\pi\ ft[/tex]The new circumference is equal to[tex]C=\pi (4)[/tex][tex]C=4\pi\ ft[/tex]Divide [tex]\frac{4\pi}{(1/2)\pi}=8[/tex]sothe new circumference will be the original circumference multiplied by 8Part D) The new circumference will be 64 times the original circumferenceThe statement is falseBecause, the new circumference will be 8 times the original circumference (see part C)Part E) The new area will be 8 times the original areaThe statement is falsewe know thatIf two figures are similar, then the ratio of its areas is equal to the scale factor squaredThe scale factor is 8soThe scale factor squared is 8²=64thereforeThe new area will be 64 times the original areaPart F) The new area will be 64 times the original areaThe statement is true(see Part E)Part G) The new circumference will be 8π feetThe statement is falseBecause, the new circumference will be 4π feet (see part C)Part H) The new area will be 16π square feetThe statement is trueBecauseThe area of a circle is[tex]A=\pi r^{2}[/tex]we have[tex]r=4\ ft[/tex]substitute[tex]A=\pi (4)^{2}[/tex][tex]A=16\pi\ ft^{2}[/tex]