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2 years ago

The cone shown has a radius of 6 inches and a slant height of 10 inches. What is the total surface area of the cone?

Mathematics

1 answer:

gogolik [260]2 years ago

6 0

Answer:

$A=301.71\ \text{inches}^2$

Step-by-step explanation:

Given that,

The radius of a cone, r = 6 inches

The slant height of the cone, l = 10 inches

We need to find the total surface area of the cone. It is given by :

$A=\pi rl+\pi r^2$

Substituting all the values,

$A=\pi r(l+ r)\\\\A=\dfrac{22}{7}\times 6\times (10+ 6)\\\\A=301.71\ \text{inches}^2$

So, the total surface area of the cone is $301.71\ \text{inches}^2$ .

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Let $7^{x-2} = 149$ , we proceed to find its equivalent expression by applying logarithm properties:

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1. To find for the linear function from this problem, we use the formula:

x/a + y/b = 1

where a is the x intercept and b is the y intercept

x/-9 + y/3 = 1

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x – 3y = -9

Rearranging:

3y = x + 9

y = (1/3) x + 3

2. The general form of a linear function is:

y = mx + b

where m is the slope and b is the y-intercept

y = (-2/5) x + b

when y = 0, x = 1 therefore the b is:

0 = -2/5 + b

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y = (-2/5) x + 2/5

3. We create two equations from the general form y = mx + b or f(x) = mx + b

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5 = -1/3 m

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y = -15x + b

using any pair to get the value of b:

-5 = -15 (1/6) + b

b = -2.5

y = -15x – 2.5

4. same steps with number 3

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2 = (2/3) m + b

Subtract the two equations:

-2/3 - 2 = (1 – 2/3) m

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using any pair to get the value of b:

2 = -8(2/3) + b

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y = -8x + 22/3

5. From the graph we have the points:

(-5, 4) and (4, -4)

So we create two equations:

4 = (-5) m + b

-4 = (4) m + b

Subtract the two equations:

4 - -4 = (-5 - 4) m

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m = -8/9

y = (-8/9) x + b

using any pair to get the value of b:

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-5 = (2) m + b

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Subtract the two equations:

-5 - 6 = (2 - 4) m

-11 = -2 m

m = 5.5

y = 5.5 x + b

using any pair to get the value of b:

-5 = 5.5 (2) + b

b = -16

y = 5.5 x – 16

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