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tangare [24]
3 years ago
11

A solid piece of wood shaped as a cylinder with an 8-centimeter diameter is cut as shown. What is the surface area of the figure

? Express the answer in terms of π.
Mathematics
1 answer:
aliina [53]3 years ago
6 0
The surface area of the figure is 96 + 64π ⇒ 1st answer
Step-by-step explanation:
* Lats revise how to find the surface area of the cylinder
- The surface area = lateral area + 2 × area of one base
- The lateral area = perimeter of the base × its height
* Lets solve the problem
- The figure is have cylinder
- Its diameter = 8 cm
∴ Its radius = 8 ÷ 2 = 4 cm
- Its height = 12 cm
∵ The perimeter of the semi-circle = πr
∴ The perimeter of the base = 4π cm
∵ The area of semi-circle = 1/2 πr²
∴ The area of the base = 1/2 × π × 4² = 8π cm²
* Now lets find the surface area of the half-cylinder
- SA = lateral area + 2 × area of one base + the rectangular face
∵ LA = perimeter of base × its height
∴ LA = 4π × 12 = 48π cm²
∵ The dimensions of the rectangular face are the diameter and the
height of the cylinder
∴ The area of the rectangular face = 8 × 12 = 96 cm²
∵ The area of the two bases = 2 × 8π = 16π cm²
∴ SA = 48π + 16π + 96 = 64π + 96 cm²
* The surface area of the figure is 96 + 64π
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Answer:

y=x+4

Step-by-step explanation:

So, let's start with the fact that we have two numbers. Let's call one of them "x" and the other one "y." Let's also assume that "y" is the larger number and "x" is the smaller number.

 

We know that both of them added together (the sum) gives us 74. Mathematically, that means:

 

x+y=74.

 

We also know that the larger number ("y") is 4 more than the smaller number ("x"). Another way to say this is, if you have the smaller number and add 4 more to it, you'll end up with the larger number. Mathematically, this means:

 

y=x+4

 

Since we know that y=x+4, we can put "x+4" into the first equation for "y", giving us:

 

x+(x+4)=74

 

Simplifying gives us:

 

2x+4=74

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  ---------

2x=70

---  ---

2    2

 

 

x=35

 

Since we now know that x=35, and we know that y=x+4, we now know that:

 

y=(35)+4

y=39

 

Now that we have both of the numbers, we should check our work to ensure it's correct:

 

Does 39+35=74?      Yes it does.

 

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Answer:

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Step-by-step explanation:

we know that

The simple interest formula is equal to

I=P(rt)

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

Let

x ------> the amount of money that should be invested at the rate of 5.25%

25,000-x -----> the amount money that should be invested at the rate of 4%

in this problem we have

t=1\ year\\ P_1=\$x\\P_2=\$(25,000-x)\\r_1=0.0525\\r_2=0.04\\I=\$1,150

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The amount of money that should be invested at the rate of 5.25% is $12,000 and the amount money that should be invested at the rate of 4% is $13,000

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