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The sphere below has a radius of 2.5 inches and an approximate volume of 65.42 cubic inches.



Note: Figure is not drawn to scale.

A second sphere has twice the radius of the given sphere. A third sphere has a diameter that is three-fourths of the diameter of the given sphere.

Complete the statements below. Use 3.14 for .

The radius of the second sphere is
inches.

The approximate volume of the second sphere to two decimal places is
cubic inches.

The radius of the third sphere is
inches.

The approximate volume of the third sphere to two decimal places is
cubic inches.

Respuesta :

Part a: The radius of the second sphere is 5 inches.

Part b: The volume of the second sphere is 523.33 in³

Part c; The radius of the third sphere is 1.875 inches.

Part d: The volume of the third sphere is 27.59 in³

Explanation:

Given that the radius of the sphere is 2.5 inches.

Part a: We need to determine the radius of the second sphere.

Given that the second sphere has twice the radius of the given sphere.

Radius of the second sphere = 2 × 2.5 = 5 inches

Thus, the radius of the second sphere is 5 inches.

Part b: we need to determine the volume of the second sphere.

The formula to find the volume of the sphere is given by

[tex]V=\frac{4}{3} \pi r^3[/tex]

Substituting [tex]\pi=3.14[/tex] and [tex]r=5[/tex] , we get,

[tex]V=\frac{4}{3} (3.14)(125)[/tex]

[tex]V=\frac{1580}{3}[/tex]

[tex]V=523.3333 \ in^3[/tex]

Rounding off to two decimal places, we have,

[tex]V=523.33 \ in^3[/tex]

Thus, the volume of the second sphere is 523.33 in³

Part c: We need to determine the radius of the third sphere

Given that the third sphere has a diameter that is three-fourths of the diameter of the given sphere.

Hence, we have,

Diameter of the third sphere = [tex]\frac{3}{4} (5)=3.75[/tex]

Radius of the third sphere = [tex]\frac{3.75}{2} =1.875[/tex]

Thus, the radius of the third sphere is 1.875 inches

Part d: We need to determine the volume of the third sphere

The formula to find the volume of the sphere is given by

[tex]V=\frac{4}{3} \pi r^3[/tex]

Substituting [tex]\pi=3.14[/tex] and [tex]r=1.875[/tex] , we get,

[tex]V=\frac{4}{3} (3.14)(1.875)^3[/tex]

[tex]V=\frac{4}{3} (3.14)(6.59)[/tex]

[tex]V=27.5901 \ in^3[/tex]

Rounding off to two decimal places, we have,

[tex]V=27.59 \ in^3[/tex]

Thus, the volume of the third sphere is 27.59 in³

Answer:

Step-by-step explanation:

Part a: The radius of the second sphere is 5 inches.

Part b: The volume of the second sphere is 523.33 in³

Part c; The radius of the third sphere is 1.875 inches.

Part d: The volume of the third sphere is 27.60 in³

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