All categories

3 years ago

What is the scale factor of two similar pyramids with volume of 13824 cubic feel and 216 cubic feet?

Mathematics

1 answer:

velikii [3]3 years ago

3 0

Answer: The scale factor is 4

Step-by-step explanation:

We know that the pyramids are similar. The volume of one of these pyramids is 13,824 cubic feet and the volume of the other one is 216 cubic feet. Then:

$V_1=13,824ft^3\\V_2=216ft^3$

By Similar solids theorem, if two similar solids have a scale factor of $\frac{a}{b}$ , then corresponding volumes have a ratio of $\frac{a^3}{b^3}$

Then:

$\frac{V_1}{V_2}=\frac{a^3}{b^3}$

Knowing this, we can find the scale factor. This is:

$\frac{13,824}{216}=\frac{a^3}{b^3}\\\\\frac{13,824}{216}=(\frac{a}{b})^3\\\\\frac{a}{b}=\sqrt[3]{\frac{13,824}{216}}\\\\scale\ factor=\frac{a}{b}=4$

You might be interested in

Please help with these questions... I've been trying to figure them out for like twenty minutes and at this point I just don't h

vlada-n [284]

Answer:

1. y=2x^2-8X-1

2. y=-6x^2+36x-63

3. y=-3x^2+18x-34

4. y=9x^2+54x+76

5. y=-x^2+8x-22

6. y=6x^2-48x+90

7. y=8x^2+16x+5

8. y=2x^2-8x+1

Have a great day :)

3 0

3 years ago

Please help

ehidna [41]

Answer:

The length between the two points is RT = 1.3 units

Step-by-step explanation:

The coordinates of the point R and T are R(2,1.2) and T(2,2.5).

Now, by DISTANCE FORMULA:

The distance between two coordinates P and Q with coordinate P(a,b) and Q(c,d) is given as:

$PQ = \sqrt{(a-c)^2 + (b-d)^2}$

So, here the distance RT = $\sqrt{(2-2)^2 + (2.5 - 1.2)^2} = \sqrt{0^2 + (1.3)^2} = 1.3$

or, RT = 1.3 units

Hence, the length between the two points is RT = 1.3 units

6 0

3 years ago

The area of a rectangle with 2 1/2 as the width and 10 feet as the length

Tanya [424]

The formula for the area of a rectangle is:
$A=wl$
w = width
l = length

First, we have to convert 2 $\frac{1}{2}$ into an improper fraction, then into a number. The improper fraction would be $\frac{5}{2}$ . Let's convert that into a decimal.
$5/2=2.5$

Let's multiply
$2.5*10=25$
The area of the rectangle would be 25 feet!

7 0

3 years ago

Lucy graphed the equations x + 9 y = 5 and 4 x + 15 y = negative 1 and saw that they intersected at the point (–4, 1) as shown.

aleksandrvk [35]

Answer: A

Step-by-step explanation:

You can solve a system of equations by graphing, elimination, substitution, or using a combination. The graph of a linear equation is a line. The point(s) where one line intersects another is the solution to the system. Therefore, since Lucy found that the lines intersected at the point (-4, 1), it is the solution to the system of linear equations

7 0

2 years ago

Four friends each bought a movie ticket and two boxes of candy at a movie theater. The tickets were $ 7.50 and the boxes of cand

777dan777 [17]

Subtract the cost of tickets from the total. 4x7.5=30. 58-30=28. Eight boxes of candy were purchased in total. Use c to represent candy. 8c=28. Finally, divide both by 8. 28/8= 3.5. The answer is $3.50.

6 0

4 years ago

Read 2 more answers