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Dmitrij [34]
3 years ago
14

A hemispherical depression is cut out from one face of a cuboidal wooden block of edge 21cm such that the diameter of the hemisp

here is equal to the edge of the cube. Determine the total surface area of the remaining block
Mathematics
2 answers:
Mandarinka [93]3 years ago
4 0

Answer:

  (2646 +110.25π) cm² ≈ 2992.4 cm²

Step-by-step explanation:

The area of a sphere is 4 times the area of a circle with the same radius. Hence the area of a hemisphere will be 2 times the area of that circle. This means carving a hemispherical depression in the face of the cube will add an area that is equal to the area of the circular hole.

Of course the total surface area of a cube is 6 times the area of one square face. The area of a circle is ...

  A = πr² = π(d/2)² = (π/4)d²

The total surface area of the carved cube is ...

  S = 6·(21 cm)² + (π/4)·(21 cm)² = (441 cm²)(6 +π/4)

  S ≈ 2992.36 cm²

The total surface area of the remaining block is about 2992.4 cm².

joja [24]3 years ago
4 0

Answer:

(2646 +110.25π) cm² ≈ 2992.4 cm²

Step-by-step explanation:

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A model for the density δ of the earth’s atmosphere near its surface isδ=619.09−0.000097pwhere p (the distance from the center o
natta225 [31]

Answer: 3.751*10^18kg

Step-by-step explanation:

δ =619.09−0.000097p....equa1 where p (the distance from the center of the earth) is measured in meters and δ is measured in kilograms per cubic meter.

Calculating the density of air at 5km above earth surface

P = 5000m + 6370000m = 6.375*10^6m

δ = 619.09 -(.000097* 6.375*10^6)

δ = 0.715kg/m^3 = density

Since Mass = density*volume...equ2

To calculate volume of air around the spherical earth at height 5km

V = (4/3 pai R^3) - (4/3pai r^3) ...equation 3 where R =6.375*10^6m, r = 6.37*10^6

Substituting R and r in equation 2 to solve for volume of air

V = 1.085*10^21 - 1.08*10^21

V = 5.25*10^18m^3

Substituting δ and V into equation 2 to solve for mass of air

M = 0.715 * (5.25*10^18)

M = 3.751*10^18kg

8 0
3 years ago
Does the equation 7c+8p=29.60 help us to solve the original system? 5c+4p=18.40 2c+4p=11.20 If you think so, explain how it help
garik1379 [7]

Step-by-step explanation:

Given the simultaneous equation

5c+4p=18.40 ..... 2

2c+4p=11.20.......2

According to the equation given  7c+8p=29.60, we will see that the two equation was added to get the required equation in question. Note that this equation  7c+8p=29.60 cannot help us to solve the simultaneous equation because the resulting equation is one equation with two unknown variables. For us to get a solution to the simultaneous equation, we need to reduce the system of equation to just an equation and a variable. This can be gotten by taking the difference of the two equation as shown: (Elimination method)

Equation 1 - equation 2 will give;

(5c-2c)+(4p-4p) = 18.40-11.20

3c+0 = 29.60

3c = 29.60

Divide both sides by 3

3c/3 = 29.60/3

c = 9.87

Substitute c = 9.87 into equation 2

From 2: 2c+4p = 11.20

c + 2p = 5.60

9.87 + 2p = 5.60

2p = 5.60 - 9.87

2p= -4.27

p = -4.27/2

p = -2.135

You can see that what helped in solving the system of equation is by eliminating one of the variables first using the Elimination method.

8 0
3 years ago
What is the missing length?<br> с<br> 4 mm<br> 3 mm<br> 2<br> area = 10 mm
Anarel [89]

Answer:

4mm

Step-by-step explanation:

That is the answer thank you hehehe

3 0
3 years ago
PLEASE HELP ASAP ON THIS PROBLEM
hjlf

Answer:

The ball was dropped from 150 feet.

It will take the ball 3.06 seconds to reach the ground.

Step-by-step explanation:

A story is 10 feet.

You want to find the number of seconds for the ball to reach the ground, which is a height of 0.  So you can put 0 in for h(t), and then solve that.  If you need more help than that, let me know.

7 0
3 years ago
Is 10 irrational or rational
aev [14]
The number 10 Is Rational
5 0
3 years ago
Read 2 more answers
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