All categories

1 year ago

If XY is 4 m and WZ is 9 m, the exact volume of the cone is ___ pi square meters

Mathematics

1 answer:

Butoxors [25]1 year ago

7 0

Volume of the cone =

$\frac{1}{3}\pi r^2h$ $=\frac{1}{3}\times\pi\times3^2\times9=3^3\pi=27\pi\text{ square meters}$

You might be interested in

A ladder 10 m long,leans against a vertical wall at an angle of 70° to the ground.if the ladder slips down the wall 4m,find,corr

lina2011 [118]

Answer:

(a) the new angle the ladder makes with the ground is $32.7^o$

(b) the ladder slipped back about 5 meters

Step-by-step explanation:

Notice that the ladder doesn't change its length in the process.

So let's start from the initial situation , finding the distance from the ground at which the ladder touches the wall when the angle with the ground is 70^o. Notice that this situation is represented by a right angle triangle with the right angle between the wall and the ground (see attached image), and that we can use the sine function to find the side opposite to the 70 degree angle:

$sin(70^o)=\frac{opposite}{hypotenuse} \\sin(70^o)=\frac{h}{10}\\h=10\, sin(70^o) \approx 9.4 \,\,m$

therefore 9.4 meters is approximately the height at which the ladder touches the wall initially.

Now, if the tip of the ladder goes down the wall 4 meters, it is now at 9.4 m - 4 m = 5.4 m from the ground. We can therefore use again the sine function to solve for the new angle:

$sin(x)=\frac{opposite}{hypotenuse} \\sin(x)=\frac{5.4}{10} \\sin(x)=0.54\\x=arcsin(0.54)\\x= 32.7^o$

To answer the second question we need to find the original distance from the wall that the bottom of the ladder was originally, and for that we can use the cosine function:

$cos(70^o)=\frac{adjacent}{hypotenuse} \\cos(70^o)=\frac{x}{10}\\x=10\,cos(70^o)\\x\approx 3.4 \,\,m$

Now fro the new position of the bottom of the ladder relative to the wall:

$cos(32.7^o)=\frac{adjacent}{10} \\adjacent=10\,cos(32.7^o)\\adjacent\approx 8.4\,\,m$

then the difference in between those two distances is what we need:

8.4 m - 3.4 m = 5 m

4 0

3 years ago

Help with math thanks so much!!!!

KatRina [158]

Answer:

0.2

Step-by-step explanation:

14/10÷x=7

14/10=7x

1.4±7=x

x=0.2

6 0

3 years ago

Explain what the slope of a linear relationship is.

Brums [2.3K]

The slope is the same as rate of change. In a linear graph, it is the change in y over the change in x.

8 0

3 years ago

There are 14 girls and 2 boys taking karate lessons. Write the ratio that compares the number of girls taking karate lessons to

Delvig [45]

Answer:

The correct answer is 7 : 8.

Step-by-step explanation:

There are 14 girls and 2 boys taking karate lessons.

Total number of students taking the karate class is 16.

The ratio that compares the number of girls taking karate lessons to the total number of students taking karate lessons is given by 14 : 16 = 7 : 8.

This can be interpreted as for every 8 students in the karate lesson, 7 of them are girls.

8 0

3 years ago

|4a|=20<br> PLEASE HELPPPPPPPPPP

fgiga [73]

Answer:

The answer to |4a|=20 is a=5 or a=-5.

Step-by-step explanation:

6 0

3 years ago