Answer:
Option c.) the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.
Step-by-step explanation:
step 1
Find the volume of one ball
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=1.5\ in[/tex]
[tex]V=\frac{4}{3}(3.14)(1.5)^{3}=14.13\ in^{3}[/tex]
therefore
The volume of two balls is
[tex](2)*14.13=28.26\ in^{3}[/tex]
step 2
Find the volume of the cylinder
The volume of the cylinder is equal to
[tex]V=\pi r^{2}h[/tex]
we have
[tex]r=1.5\ in[/tex]
[tex]h=1.5*4=6\ in[/tex]
substitute
[tex]V=(3.14)(1.5)^{2}(6)=42.39\ in^{3}[/tex]
therefore
The wasted space with the cylinder is equal to
[tex]42.39\ in^{3}-28.26\ in^{3}=14.13\ in^{3}[/tex]
step 3
Find the volume of the square prism
The volume of the square prism is equal to
[tex]V=b^{2}h[/tex]
we have
[tex]b=1.5*2=3\ in[/tex]
[tex]h=1.5*4=6\ in[/tex]
substitute
[tex]V=(3)^{2}(6)=54\ in^{3}[/tex]
therefore
The wasted space with the prism is equal to
[tex]54\ in^{3}-28.26\ in^{3}=25.74\ in^{3}[/tex]
step 4
Find the difference of the wasted space
[tex]25.74\ in^{3}-14.13\ in^{3}=11.61\ in^{3}[/tex]
Answer:
C. the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.
Step-by-step explanation:
if you find the volumes of both shapes and subtract the volumes of the two balls and then subtract the two remaining values you get a difference of 11.6 inches. This makes the cylinder smaller and therefore uses less space.
