Answer:
Part 42) The surface area of the sphere is [tex]SA=795.8\ ft^{2}[/tex]
Part 43) The surface area of the sphere is [tex]SA=1,781.6\ m^{2}[/tex]
Part 44) The scale factor is [tex]\frac{19}{9}[/tex]
Step-by-step explanation:
Part 42) What is the surface area of a sphere with a circumference of 50 feet round the answer to the nearest 10th
step 1
Find the radius of the sphere
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=50\ ft[/tex]
assume
[tex]\pi =3.14[/tex]
substitute and solve for r
[tex]50=2(3.14)r[/tex]
[tex]r=7.96\ ft[/tex]
step 2
Find the surface area of the sphere
The surface area of the sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
substitute the value of r
[tex]SA=4(3.14)(7.96)^{2}[/tex]
[tex]SA=795.82\ ft^{2}[/tex]
round to the nearest 10th
[tex]795.82=795.8\ ft^{2}[/tex]
Part 43) The volume of a sphere is 2254 pi m^3. What is the surface of the sphere to the nearest 10th?
step 1
Find the radius of the sphere
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]V=2,254\pi\ m^{3}[/tex]
substitute and solve for r
[tex]2,254\pi=\frac{4}{3}\pi r^{3}[/tex]
Simplify
[tex]1,690.5=r^{3}[/tex]
[tex]r=11.91\ m[/tex]
step 2
Find the surface area of the sphere
The surface area of the sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
substitute the value of r
[tex]SA=4(3.14)(11.91)^{2}[/tex]
[tex]SA=1,781.6\ m^{2}[/tex]
Part 44) What is the scale factor of a cube with a volume of 729 m^3 to a cube with a volume of 6859?
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
so
Let
z -----> the scale factor
x ----> the volume of the larger cube
y ----> the volume of the smaller cube
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]x=6,859\ m^{3}[/tex]
[tex]y=729\ m^{3}[/tex]
substitute
[tex]z^{3}=\frac{6,859}{729}[/tex]
[tex]z=\frac{19}{9}[/tex]
[tex](\frac{6,859}{729})[/tex]
