Question

PLEASE HELP ASAP!!

At a frozen yogurt store, customers can purchase gelatin spheres as a yogurt topping. Each sphere contains 100.48/3 cubic millimeters of gelatin. Which statements about the measurements of the sphere are true? Check all that apply. (Use 3.14 for π. Recall that the formula for the volume for a sphere is V= 4/3πr³ .)

The radius of a sphere is 8 millimeters.
The radius of a sphere is 2 millimeters.
The circumference of the great circle of a sphere is 9.42 square millimeters.
The surface area of a sphere is 50.24 square millimeters.
The circumference of the great circle of a sphere is 12.56 square millimeters.
The surface area of a sphere is 25.12 square millimeters.

Answer 1

B, D,E

Explanation:

Answer 2

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.

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

`V=(4)/(3)\pi r^(3)`

we have

`V=100.48/3\ mm^(3)`

`\pi =3.14`

substitute and solve for r

`100.48/3=(4)/(3)(3.14)r^(3)`

`r^(3)=(100.48)/(4*3.14)`

`r=2\ mm`

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

`C=2\pi r`

we have

`r=2\ mm`

`\pi =3.14`

substitute

`C=2(3.14)(2)`

`C=12.56\ mm`

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

`SA=4\pi r^(2)`

we have

`r=2\ mm`

`\pi =3.14`

substitute

`SA=4(3.14)(2)^(2)`

`SA=50.24\ mm^(2)`

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
`SA=50.24\ mm^(2)`

see the case D