Answer:
The radius of a sphere is 2 millimeters
The surface area of a sphere is 50.24 square millimeters.
The circumference of the great circle of a sphere is 12.56 millimeters.
Step-by-step explanation:
Verify each statement
case A) The radius of a sphere is 8 millimeters
The statement is false
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]V=100.48/3\ mm^{3}[/tex]
[tex]\pi =3.14[/tex]
substitute and solve for r
[tex]100.48/3=\frac{4}{3}(3.14)r^{3}[/tex]
[tex]r^{3}=(100.48)/(4*3.14)[/tex]
[tex]r=2\ mm[/tex]
case B) The radius of a sphere is 2 millimeters
The statement is True
(see the case A)
case C) The circumference of the great circle of a sphere is 9.42 square millimeters
The statement is false
The units of the circumference is millimeters not square millimeters
The circumference is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=2\ mm[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]C=2(3.14)(2)[/tex]
[tex]C=12.56\ mm[/tex]
case D) The surface area of a sphere is 50.24 square millimeters.
The statement is True
Because
The surface area of the sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
we have
[tex]r=2\ mm[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]SA=4(3.14)(2)^{2}[/tex]
[tex]SA=50.24\ mm^{2}[/tex]
case E) The circumference of the great circle of a sphere is 12.56 millimeters.
The statement is true
see the case C
case F) The surface area of a sphere is 25.12 square millimeters
The statement is false
because the surface area of the sphere is [tex]SA=50.24\ mm^{2}[/tex]
see the case D
