To calculate the volume of this figure, we just have to find the volume of the hemisphere and the volume of the cone, then sum them up.
The volume of a hemisphere (the half of a sphere) is given by the formula:
Where r is the radius.
The volume of a cone is given by the formula:
Where h is the height of the cone.
From the figure we have:
r = 5.3in
h = 9 in
Then, when we substitute these values into the above formulas, we get:
For the hemisphere:
The volume of the hemisphere is 311.6in^3
For the cone:
As mentioned, the volume of the whole figure is the sum of the volume of the cone and the volume of the hemisphere, then, the volume of the figure is:
V=311.6in^3 + 264.7in^3 = 576.3in^3
Then, the correct answer is option A
It equals 0.003472222222222
Answer:
x = -2; or x = -8
Step-by-step explanation:
Solve the quadratic function by completing the square. What are the missing pieces in the steps? -32=2(x^2+10)
-32+___=2(x2+10x+25)
18=2(x+5)^2
9=(x+5)^2
+-___=x+5
X=-2 or x=___
Solution:
From the first line:
-32+___=2(x2+10x+25)
Also, in the second line:
18=2(x+5)^2
Let the missing piece on line 2 be a, hence:
x² + 10x + 25 = (x + 5)² and -32 + a = 18
a = 18 + 32 = 50
-32 + 50 =2(x²+10x+25)
18 = 2(x+5)²
Dividing through by 2:
18 / 2= [2(x+5)² / 2]
9 = (x + 5)²
Taking square root of both sides:
√9 = √(x + 5)²
± 3 = x+5
Simplifying the equation to get:
3 = x + 5; -3 = x + 5
x = 3 - 5; or x = -3 - 5
x = -2; or x = -8
Check the picture below.
a bisector, means, it "cuts in two equal halves".
Answer:
28.137 sq. units.
Step-by-step explanation:
Area of a regular hexagon is
where, a is the side length.
It is given that the side length of the regular hexagon is 
.
Substitute 
in the above formula.
Therefore, the area of regular hexagon is 28.137 sq. units.
