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slega [8]
3 years ago
5

Find the volume of the hemisphere shown. remember a hemisphere is half of a sphere. r = 5

Mathematics
1 answer:
jenyasd209 [6]3 years ago
3 0
As we know from geometry, the volume of any given sphere is

V = 4/3*πr³

Since a hemisphere is half of any given sphere, its volume should be

V = 4/3*πr³ ÷ 2
V = 2/3*πr³

This will be our working equation for finding the volume of hemisphere. Since r is already given to be 5 units, we substitute this to the working equation:

V = 2/3*π(5)³
V = 261.8 cubic units
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The sides of a square are 3 2/7 inches long.<br> What is the area of the square?
vredina [299]
Area is just height times width so if it’s a square all sides are equal so you do 3 2/7 time 3 2/7 and get 10.796 in^2
3 0
3 years ago
Surface Area of the pyramid
hichkok12 [17]

Answer:

C

Step-by-step explanation:

the total surface area of such a pyramid is the sum of 5 areas :

1 bottom square (8×8)

4 side triangles

the area of a triangle is

baseline × height / 2

now, we know the baseline of the 4 triangles, but what is their height (at least we know, all 4 have the same height, as the pyramid is totally regular) ?

the height of the side triangles is the slant height of the pyramid (the distance from the middle of a sideline to the top of the pyramid).

we get this by imagining a right-angled triangle inside the pyramid :

one leg is the inner height of the pyramid.

the second leg is the connection on the bottom square from the base of the inner height to the middle point of a sideline). this is half the length of a sideline.

and the baseline (Hypotenuse) is the slant height of the pyramid.

we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle).

slant height² = 7² + (8/2)² = 49 + 4² = 49 + 16 = 65

slant height = sqrt(65) = 8.062257748... in

so, we get a areas

bottom square = 8×8 = 64 in²

a side triangle = 8×sqrt(65)/2 = 4×sqrt(65) =

= 32.24903099... in²

all 4 side triangles = 4×32.24903099... =

= 128.996124... in²

and we get as total surface area

64 + 128.996124... = 192.996124... in² ≈ 193.00 in²

8 0
2 years ago
Find the measure of the remote exterior angle. m∠x=(4n−18)°m∠y=(n+9)°m∠z=(151−5n)° A. 71 B. 16 C. 100 D. 46
devlian [24]

Answer: A.71

Step-by-step explanation: 1.set up the equation

2. 4n-18+n+9=151-5n

3.combine like terms ->  5n-9=151-5n

4.solve for n

5.10n=160

n=16

now you have to plug 16 in for n in order to get the remote exterior angle.

151-5(16)

151-80

71°

7 0
3 years ago
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Write an equation that represents the area of Shannon’s garden
natulia [17]
If Shannon's garden is in a rectangle, the area of a rectangle is (length x width). If it's a square, then it would simply be (length x length) ... or length squared.
5 0
3 years ago
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