The volume of the space not filled by the sphere is the difference between the volume of a cube with edge length 6 inches and the volume of a sphere with radius 3 inches.
<h3><u>Cube</u></h3>
The volume of a cube of edge length s is
... V = s³
When the edge length is 6 in, the volume is
... V = (6 in)³ = 216 in³
<h3><u>Sphere</u></h3>
The volume of a sphere with radius r is
... V = (4/3)π·r³
When the radius is 3 in, the volume is
... V = (4/3)π·(3 in)³ = 36π in³
<h3><u>Space</u></h3>
Then the volume of the space between the cube and the sphere is
... Vcube - Vsphere = 216 in³ - 36π in³ ≈ 102.9 in³ . . . . corresponding to choice C
Answer:
The total area of the figure is 52 in²
Step-by-step explanation:
This figure requires you to find the area of the square and the triangle separately, and then subtract the area of the triangle from the area of the square.
Find the area of the square
l=8in
A=l²
A=8²
A=64 in²
The area of the square is 64 in²
Find the area of the triangle
b=8in
h=3in
A=(bh)/2
A=(8*3)/2
A=24/2
A=12 in²
The area of the triangle is 64 in²
Now we need to subtract the areas
64-12=52 in²
The total area of the figure is 52 in²
Midsegments are line segments that connect the midpoints of a triangle. If we have the condition that QR = NP, we have the equation
3x + 2 = 2x + 16
Solving for x
3x - 2x = 16 - 2
x = 14
Therefore, x is 14. <span />
Answer:
PQ=30
Step-by-step explanation:
Knowing that the segment has 3 parts that are 3:1:1 and sum up to 50, you could find how much 1 would equal by finding the total in relation to the ratio (doing 3+1+1) which gets you 5 parts. Then you can divide the total (50) by 5 to figure out how much one part would equal (10). Now, since you know that 1 part is equal to 10 and that PQ is 3 parts, you can find that PQ is equal to 3x10, or 30.
