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Elanso [62]
4 years ago
10

The height of a pyramid-shaped sculpture with a square base is one half the length of each side. The volume of the sculpture is

972 in^3. What is the height of the sculpture?
I need the answer asap!!
Mathematics
1 answer:
Nimfa-mama [501]4 years ago
4 0

The volume of a pyramid is V = 1/3 x base length^2 x height

Let X = base length.

We are told the height is 1/2 the length, so height would be 1/2x

Now we have:

972 = 1/3 * x^2 * 1/2x

Simplifying we get:

972 = 1/6x^3

Multiply both sides by 6:

5832 = x^3

Take the cube root of both sides:

x = 18

The length of the base is 18 inches.

The height is 1/2 that, so the height would be 18/2 = 9 inches.

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Step-by-step explanation:

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Answer:

Dilate circle A by a scale factor of 4.

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3 years ago
Problem 9
lapo4ka [179]

Answer:

3:36PM

Step-by-step explanation:

Leon starts at 12PM with 12 gallons of gas, and after 2 hours he has used 5 gallons of gas. This means that every 2 hours he uses 5 gallons of gas.

Next we will find at what point Leon will stop to get gas. Since he will stop when the tank is at \frac{1}{4} capacity, we can use the equation:

\frac{1}{4} * 12 = \boxed{3}

This shows \frac{1}{4} of his tank's capacity (12) is equal to 3 gallons. This means he will stop for gas when 3 gallons are remaining.

Now we need to find how many gallons of gas he uses, but as a unit rate. (This will allow us to find what time Leon will stop to get gas.) To find the unit rate, we will need to find how many gallons of gas he uses per hour.

\frac{\mbox{5 gallons}}{\mbox{2 hours}} = \frac{\mbox{2.5 gallons}}{\mbox{1 hours}}

This is a simple proportion, and now we know he uses 2.5 gallons of gas per hour.

Now we can how many hours of gas Leon has left.

He has 7 gallons of gas left at 2PM, so we can divide to find how many hours left of gas he has.

\frac{7-3}{2.5} = 1.6

The 7-3 is because Leon doesn't stop when his tank is empty, he stops 3 gallons earlier. We are dividing by 2.5 because that is how much gas he uses per hour, meaning the result of this division (1.6) is how many hours he has left.

Now we can solve for what time Leon will stop to get gas.

12PM + 2 hours of driving + the remaining 1.6 hours = 3:36PM

(1.6 hours is equal to 1 hour and 36 minutes)

Therefore, Leon will stop for gas at 3:36PM

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Answer:

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