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3 years ago

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For her presentation on the Wonders of the World, Mary baked a square pyramid-shaped cake as pictured below. The slant height of

the cake is 10 inches. Each edge of the square-shaped base is 8 inches. Find the volume of Mary's cake. Round your answer to the nearest cubic inch.

1 answer:

miskamm [114]3 years ago

6 0

Answer:

volume = 195.52 in³

Step-by-step explanation:

given data

slant height of the cake = 10 inches

base length = 8 inches

solution

we know that volume pyramid is express as

volume = $\frac{A^2\times h}{3}$ ..............1

here

we use pythagoras for height

hypotenuse² = side1² + side2²

put here value with other side is half of a square side

10² = h² + 4²

solve it we get

h = 9.165 in

so put here value in equation 1 we get

volume = $\frac{8^2\times 9.165}{3}$

volume = 195.52 in³

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1) Members at a yoga school pay $10 per class plus a one-time $100 membership fee. Non-members pay$15 per class. How many classe

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Part 1) The number of classes must be greater than 20

Part 2) see the explanation

Part 3) $\$68.76$

Part 4) $\$12\ per\ hour$

Part 5) The equation that can be used is $27x=242.73$ and the cost of one print is $\$8.99$

Part 6) The number of classes must be greater than 30

Step-by-step explanation:

Part 1) we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

<em>Members</em>

The slope is $m=\$10\ per\ class$

The y-intercept is $b=\$100$

so

$y=10x+100$ ----> equation A

<em>Non-Members</em>

The slope is $m=\$15\ per\ class$

so

$y=15x$ ----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

$10x+100 < 15x$

Solve for x

subtract 10 x both sides

$100 < 15x-10x$

$100 < 5x$

Divide by 5 both sides

$20 < x$

Rewrite

$x > 20$

therefore

The number of classes must be greater than 20

Part 2) we have

The sum of 8 and 3 times a number is 23.

Let

x ----> the number

Remember that

3 times a number is the same that multiply 3 by the number ----> 3x

so

The sum of 8 and 3 times a number is 23 is the same that

$8+3x=23$

solve for x

subtract 8 both sides

$3x=23-8$

$3x=15$

Divide by 3 both sides

$x=5$

Part 3) we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost of renting a car for one day

x ----> the number of miles

we have

The slope is $m=\$0.42\ per\ mile$

The y-intercept is $b=\$36$

so

$y=0.42x+36$

For x=78 miles

substitute in the linear equation and solve for y

$y=0.42(78)+36$

$y=\$68.76$

Part 4) Let

x ----> Alice's normal hourly rate

we know that

40 hours multiplied by her normal hourly rate plus 10 hours (50 h-40 h) multiplied by 1.5 times her normal hourly rate must be equal to $660

so

The linear equation that represent this situation is

$40x+10(1.5x)=660$

solve for x

$40x+15x=660$

$55x=660$

Divide by 55 both sides

$x=\$12\ per\ hour$

Part 5) Let

x ----> the cost of one print

we know that

The cost of one print multiplied by 27 prints must be equal to $242.73

so

The linear equation is equal to

$27x=242.73$

solve for x

Divide by 27 both sides

$x=\$8.99$

Part 6) we know that

The linear equation in slope intercept form is equal to

$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

Let

y ----> the total cost

x ----> the number of classes

we have

<em>Members</em>

The slope is $m=\$7\ per\ class$

The y-intercept is $b=\$120$

so

$y=7x+120$ ----> equation A

<em>Non-Members</em>

The slope is $m=\$11\ per\ class$

so

$y=11x$ ----> equation B

To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality

$7x+120 < 11x$

Solve for x

subtract 7x both sides

$120 < 11x-7x$

$120 < 4x$

Divide by 4 both sides

$30 < x$

Rewrite

$x > 30$

therefore

The number of classes must be greater than 30

4 0

3 years ago