Answer:
(d) 944 mm³
Step-by-step explanation:
The volume of a prism is given by the formula ...
V = Bh
where B is the area of the base, and h is the distance between bases.
__
<h3>base area</h3>
Here, the base of the prism is a rectangle with a semicircle on top. The circle has a diameter of 9 mm, so a radius of 4.5 mm. The area of the semicircle is ...
A = 1/2πr² = 1/2π(4.5 mm)² ≈ 31.809 mm²
The area of the rectangle is the product of its length and width.
A = LW = (9 mm)(6 mm) = 54 mm²
So, the total base area is ...
31.809 mm² +54 mm² = 85.809 mm²
<h3>prism volume</h3>
The prism volume is this area multiplied by the length of the figure:
V = Bh = (85.809 mm²)(11 mm) ≈ 944 mm³
The volume of the figure is about 944 mm³.
Answer:
t = 17.5 f = 12
Step-by-step explanation:
If <em>MNOP </em>is a square, you know that each angle is going to be 90°. To solve, let's first set each equation equal to 90°:
and
Then solve both equations:
and
I hope that helps!
Answer: 10+20=30
Step-by-step explanation:
Answer:
<h2>x = 3 and y = 4</h2>
Step-by-step explanation:
We know:
The diagonals in a parallelogram divide by halves.
Therefore KG = UG and DG = CG.
We have
KG = 5y - 8, UG = 3y, DG = 4x - 7, CG = x + 2
Substitute:
5y - 8 = 3y <em>add 8 to both sides</em>
5y = 3y + 8 <em>subtract 3y from both sides</em>
2y = 8 <em>divide both sides by 2</em>
y = 4
---------------
4x - 7 = x + 2 <em>add 7 to both sides</em>
4x = x + 9 <em>subtract x from both sides</em>
3x = 9 <em>divide both sides by 3</em>
x = 3
Split it into 7 triangles. Half-base of each is 2 so the distance of center to the midpoint of the base is (Pythagoras) square root of (4.62 - 22) = 4.162 triangle is this times 2, and with 7 triangles multiply also by 7 to get an approximate area of 58 sq in.
