MATH SOLVE

4 months ago

Q:
# Consider this square pyramid. Recall the volume can be found using the formula V = 1/3Bh.What is the volume of the pyramid after dilating by a scale factor of 1/4? Describe the effects.A.) 16 m³. The volume of the new pyramid is the volume of the original pyramid times 1/64.B.) 64 m³. The volume of the new pyramid is the volume of the original pyramid times 1/16.C.) 256 m³. The volume of the new pyramid is the volume of the original pyramid times 1/4.D.) 1,024 m³. The volume of the new pyramid is equal to the volume of the original pyramid.

Accepted Solution

A:

Answer:Option A.) 16 m³. The volume of the new pyramid is the volume of the original pyramid times 1/64.Step-by-step explanation:step 1Find the volume of the original pyramidThe volume of the pyramid is equal to[tex]V=\frac{1}{3}Bh[/tex]whereB is the area of the baseh is the height of the pyramidwe have[tex]B=16^{2}=256\ m^{2}[/tex] ----> is the area of a square[tex]h=12\ m[/tex] substitute[tex]V=\frac{1}{3}(256)(12)[/tex][tex]V=1,024\ m^{3}[/tex]step 2Find the volume of the new pyramidwe know thatIf two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cubesoLetz -------> the scale factorx ------> the volume of the new pyramidy -----> the volume of the original pyramid[tex]z^{3}=\frac{x}{y}[/tex]we have[tex]z=\frac{1}{4}[/tex][tex]y=1,024\ m^{3}[/tex]substitute and solve for x[tex](\frac{1}{4})^{3}=\frac{x}{1,024}[/tex][tex]x=(1,024)\frac{1}{64}=16\ m^{3}[/tex]thereforeThe volume of the new pyramid is the volume of the original pyramid times 1/64