All categories

1 year ago

Complete the statements about these similar pyramids.

Mathematics

1 answer:

Goryan [66]1 year ago

5 0

The ratio of the heights of the pyramid given at the end of the answer is of: 1:3.

The ratio of the surface areas of the pyramid given at the end of the answer is of: 1:9.

The ratio of the volumes of the pyramid given at the end of the answer is of: 1:27.

<h3>How to obtain the ratios?</h3>

The first step in obtaining the ratios is finding the ratio of the heights, which is given as follows:

5:15 = 1:3.

The heights are measured in units, while the surface area is measured in units squared, hence the ratio is squared, as follows:

(1:3)² = 1:9.

The volume is measured in cubic units, hence the ratio is cubed, as follows:

(1:3)³ = 1:27.

<h3>Missing Information</h3>

The pyramid is given at the end of the answer.

For different dimensions, the procedure of taking the ratio of the heights, then the surface area is squared and the volume is cubed remains.

More can be learned about ratios of area and volume at brainly.com/question/15990299

#SPJ1

You might be interested in

How to expand and simplify (2x+3y)(x-y)

Nezavi [6.7K]

(2*x+3*y)*(x-y) this is expanded form

4 0

4 years ago

Read 2 more answers

Brock’s taxable income last year was $65,150. According to the tax table below, how much tax does he have to pay if he filed wit

gogolik [260]

Your answer should be c

4 0

4 years ago

Read 2 more answers

A girl starts to walk to her school, which is 20 miles away, at 6:50 and at a rate of 3 miles per hour. After a while, her dad p

Alexeev081 [22]

The girl walked a distance of $\boxed{{\mathbf{5 miles}}}$ in her way.

Further explanation:

The time can be calculated as,

${\text{ time}}=\frac{{{\text{distance}}}}{{{\text{speed}}}}$

Given:

It is given that a girl stands 20 miles away from the school at $6:50{\text{ am}}$ and she started walking at the rate of $3{\text{ mi/hr}}$ and then after some time her dad pick up and he drives at the rate of $30{\text{ mi/hr}}$ . They reach the school at $9:00{\text{ am}}$ .

Step by step explanation:

Step 1:

Consider $x$ as the distance she walked in her way.

The speed of the girl when she walked is $3{\text{ mi/hr}}$ .

Now use the formula of time to obtain the walk time.

$\begin{gathered}{\text{ walktime}}=\frac{{{\text{distance walked}}}}{{{\text{walking speed}}}}\hfill\\{\text{ walktime}}=\frac{x}{3}\hfill\\\end{gathered}$

Since the total distance is $20{\text{ miles}}$ .

Then consider $20-x$ as the distance driven by the car.

The driving speed is $30{\text{ mi/hr}}$ .

Now use the formula of time to obtain the drive time.

$\begin{gathered}{\text{drive time}}=\frac{{{\text{distance travelled by car }}}}{{{\text{ speed of car}}}}\hfill\\{\text{drive time}}=\frac{{20-x}}{{30}} \hfill\\\end{gathered}$

Step 2:

Now we calculate the total time took by girl to reach the school.

$9:00-6:50={\text{2 hrs 10 min}}$

Now convert the timing into hours as,

$\begin{aligned}2{\text{ hours 10 minutes}}&=2+\frac{{10}}{{60}}\\&=2\frac{1}{6}\\&=\frac{{13}}{6}{\text{ hrs}}\\\end{aligned}$

Step 3:

Total time is the sum of drive time and walk time.

The total time can be expressed as,

$\frac{x}{3}+\frac{{20-x}}{{30}}=\frac{{13}}{6}$

Now solve the above equation by cross multiply method.

$\begin{aligned}\frac{x}{3}+\frac{{20-x}}{{30}}&=\frac{{13}}{6}\hfill\\\frac{{10x+20-x}}{{30}}&=\frac{{13}}{6}\hfill\\\frac{{9x+20}}{{30}}&=\frac{{13}}{6}\hfill\\6\left({9x+20}\right)&=13\left({30}\right)\hfill\\\end{aligned}$

Now simplify the further equation.

$\begin{aligned}6\left({9x+20}\right)&=13\left({30}\right)\hfill\\54x+120&=390\hfill\\54x&=390-120\hfill\\54x&=270\hfill\\\end{aligned}$

Simplify the further equation.

$\begin{aligned}54x&=270\hfill\\x&=\frac{{270}}{{54}}\hfill\\x&=\frac{{45}}{9}\hfill\\x&=5\hfill\\\end{gathered}$

Therefore, the girl walked 5 miles.

Learn more:

Learn more about the distance between the points <u>brainly.com/question/6278187 </u>

Learn more about the equivalent fraction <u>brainly.com/question/952259 </u>

Learn more about midpoint of the segment <u>brainly.com/question/3269852 </u>

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Speed, distance and time

Keywords: girl, distance, drive, walk, drive time, dad, speed, travelled, formula, cross multiply, fraction, number, multiply, addition, subtraction, equation, school

8 0

4 years ago

Read 2 more answers

Thirty elves would like to build a skating ring so they can all use it at the same time. Santa tells them, they need at least 40

Delicious77 [7]

Answer:

The Possible dimension of the ring could be;

20 ft × 60 ft

25 ft × 48 ft

30 ft × 40 ft

60 ft × 20 ft

48 ft × 25 ft

40 ft × 30 ft

Step-by-step explanation:

Given:

Number of skaters = 30

Area for each skater = 40 sq ft

We need to find the dimension of rectangular ring the are going to build.

Now we know that they building the skating ring such that they all can use at same time.

Hence if the all use at same time then we will find the total area first.

Total area can be calculated by multiplying Number of skaters with area required for each skaters.

Framing the equation we get;

Total area = $30\times 40 = 1200 \ ft^2$

Hence The total area of the rectangular ring would be 1200 sq. ft.

Now we know that Total area is equal to product of length and width.

$length\times width =1200ft^2$

1200 can be written as = 20 × 60, 25 × 48, 30 × 40,60 × 20,48 × 25,40 × 30

Hence the Possible dimension of the ring could be;

20 ft × 60 ft

25 ft × 48 ft

30 ft × 40 ft

60 ft × 20 ft

48 ft × 25 ft

40 ft × 30 ft

3 0

3 years ago

Find the number that makes 4:12 equivalent to 28:__.

guapka [62]

Answer:

Step-by-step explanation:

We can set up a proportion using fractions.

$\frac{4}{12} = \frac{28}{x}$

Now, let's cross multiply by multiplying 12 and 28 then dividing by 4.

$12\cdot28=336\\\\336\div4=84$

Hope this helped!

6 0

3 years ago

Read 2 more answers