Select the correct answer.
1 answer:
The volume of the sphere will be 49π cubic cm. Then the correct option is C.
<h3>What is the volume of the sphere?</h3>Let r be the radius of the sphere.
Then the volume of the sphere will be
V = 4/3 πr³ cubic units
The figure shows a vertical cross-section of a sphere inscribed in a right cone.
A vertical cross-section of a sphere inside a cone has a radius labeled as r. The height of the cone is 12 centimeters. The half length of the face of the cone is 5 centimeters.
Then the volume of the sphere will be
In ΔADF, we have
tan a = 5 / 12
a = 22.61°
Then in triangle ΔABC, we have
sin 22.61° = r / (12 - r)
0.38 = r / (12 - r)
4.62 - 0.38r = r
1.38r = 4.62
r = 3.34 cm
Then the volume of the sphere will be
V = 4/3 π(3.34)³
V = 49π cubic cm
Then the correct option is C.
More about the volume of the sphere link is given below.
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The solutions to the inequality are (-∞, -3] or a ≤ -3 if the inequality −14a≥ 42 graph is shown in the picture.
<h3>What is inequality?</h3>It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
We have an inequality:
−14a ≥ 42
-a ≥ 3
a ≤ -3
a ∈ (-∞, -3]
Thus, the solutions to the inequality are (-∞, -3] or a ≤ -3 if the inequality −14a≥ 42 graph is shown in the picture.
Learn more about the inequality here:
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Given parameters:
Midpoint of AB = M(3, -1)
Coordinates of A = (5,1)
Unknown:
Coordinates of B = ?
Solution:
To find the mid point of any line, we use the expression below;
and
where and
= coordinates of the mid points = 3 and -1
x₁ = 5 and y₁ = 1
x₂ = ? and y₂ = ?
Now let us input the variables and solve,
3 = and -1 =
5 + x₂ = 6 -2 = 1 + y₂
x₂ = 1 y₂ = -2 -1 = -3
The coordinates of B = 1, -3