Answer:
<em>Option B</em>
Step-by-step explanation:
<u>Congruent Triangles</u>
The SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both triangles are congruent, then the two triangles are similar.
The triangles are congruent if the relation between LK and KN is the same as the relation between KN and MN, that is
It means that
MN=1
Option B
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
Substituting and
, we get,
Rounding off to two decimal places, we have,
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 =
Radius of the third sphere =
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
Substituting and
, we get,
Rounding off to two decimal places, we have,
Thus, the volume of the third sphere is 27.59 in³