As the word suggests, a quarter-sphere is a quarter of a sphere, and thus the volume of a quarter-sphere is a quarter of the volume of the sphere.
The volume of a sphere is computed as

So, the volume of a quarter-sphere is

 
        
             
        
        
        
Answer:
Step-by-step explanation:
The total amount of punch that Jennifer made for her party is 5 Liters. Her brother made another 750 milliliters.
1000 milliliters = 1 liter
750 milliliters = 750/1000 = 0.75Liter
if they combine the two batches, the total amount made would be 
5 + 0.75 = 5.75Liter 
= 5.75 × 1000 = 5750 milliliters
The number of 180 milliliters servings would be 
5750/180 = 31 servings
There would be leftovers of 170 milliliters
 
        
             
        
        
        
Answer:
Part A) The area of the figure is 
Part B) The perimeter of the figure is 
Step-by-step explanation:
step 1
Find the area of the figure
we know that
The area of the figure is equal to the area of triangle ABD plus the area of triangle BCD
The area of triangle is equal to

<u>Area of triangle ABD</u>
Observing the graph


substitute

<u>Area of triangle BCD</u>
Observing the graph


substitute

The area of the figure is

step 2
Find the perimeter of the figure
we know that
The perimeter of the figure is equal to

we have

the formula to calculate the distance between two points is equal to
 
Find the distance AB
 
Find the distance BC
 
Find the distance CD
 
Find the distance AD
 
substitute the values

 
        
             
        
        
        
Since we know that these two are consecutive angles and consecutive angles add up to 180 deg, we can come up with the equation 4x +5x =180. Solving this out shows us that x = 20 and the measure of angle J is 100 deg while the measure of angle M is 80 deg. 
        
             
        
        
        
Here, we are required to find the area of the paper board given after the semicircle is cut out of it
Area of the paper board thatremains is 423 in²
Length = 29 in
Width = 20 in
Area of a rectangle = length × width
= 29 in × 20 in
= 580 in²
Area of a semi circle = πr²/2
π = 3.14
r = diameter / 2 = 20 in / 2 = 10 in
Area of a semi circle = πr²/2
= 3.14 × (10 in)² / 2
= 3.14 × 100 in² / 2
= 314 in²/2
= 157 in²
The semicircle is cut out of the rectangle
Find the area of the paper board that remains after the semicircle is cut out of it by subtracting the area of a semi circle from the area of a rectangle 
Area of the paper board that remains = Area of a rectangle - Area of a semi circle
= 580 in² - 157 in²
= 423 in²
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