Volume of similar cylinders

The cylinders shown are similar.

What is the volume of the larger cylinder?

Solution:

Two chords intersect with the measures shown in the drawing.

What is the value of x?

Solution:

we know that the product of the lengths of one intersecting chord must be equal to the product of the lengths of the other, so...

For what value of x is if the lines are parallel in this figure?

Solution:

We know that x and 40.03 are supplementary, so x+40.03=180. Therefore x=139.97 degrees

Find x.

What is the value of x?

Solution:


TV is a diameter, and SU is perpendicular to TV. This means that x=8

Given quadrilateral KLMN, what is the value of x?

Given quadrilateral KLMN, what is the value of x?


Solution:

3x+x+25+80+95=360 (why?)

4x+200=360

4x=160

x=40

find the unknown length in the right triangle one side is 9m and the other side 15m.

If we assume that 15m is the longest side then a side of 12m will give us a right triangle (why?)

:)

Find the dimensions of a rectangle whose perimeter is 52 and the area is 96

then






with the solution:

Two angles are complementary. The measure of one angle is 46 degrees more than three times the measure of the other. Find the measure of each angle.

1) 
2)  

so 


 
therefore 

If the length is 3 cm and the perimeter is 10 cm, what will the width and area be? You can put this solution on YOUR website!

 

Find the perimeter and area of a rectangle whose length is 5x - 2 and width is x-3.

Which of the points A(10,4),B(7,6),C(-3,5) is nearest to P(3,-2)?

If we plot all four points carefully we can see that CP=AP
so when compared to BP they are both longer.
Therefore  is shortest

A rope 60 cm long is made to form a rectangle. if the length is four times its breath, calculate the length and diagonal of the rectangle.

which leads to

The sides of an equilatersl triangle are 3x-1, 5y, and x+13. Find the measures of each side.

equilateral => 3x-1=x+13 => x=7

and x+7 turns into 7+13=20
and so all sides are 20 units

:)

In Triangle ABC, Angle B = 15 degrees less than twice angle A and Angle C is more than angle A. Find angle C.

B=2A-15

C>A
and A+B+C=180
which becomes...
A+(2A-15)+C=180
C=180+15-3A
C=165-3A

so

Which sets our boundary to test for valid triangles. After trial and error (there's probably a better way) we can deduce the following.
The least value for C under these conditions is C=42 and the greatest is a little more than 142
so...these are pretty good approximations

 

What is the area of a circle whose circumference is π? Leave your answer in terms of π?

so

the perimeter of a rectangle is 102 inches , and the length of the diagonal is 39 inches. find the dimensions of the rectangle.

1)

P=2(l+w)=102
l+w=51

2) 

l^2+w^2=39^2

using substitution...
(l-51)^2+l^2=1521
l={15, 36}
so the dimensions are 15in x 36in

Perimeter of a rectangle if its length is (4c+7) units and its width is (c-3) units

P=
2(L+W)=
2(4c+7+c-3)=
2(5c+4)=
10c+8
where c > 3

what is the hight of a triangle with two 13 yd sides? explain?

Your Answer:

first we assume that the base is an unknown value...

if the sides are both 13 yd - the triangle must be isosceles
and from geometry we know that the height is

so in our case

The length of a rectangle is 5 inches more than double its width. If the perimeter is 70 inches, find the dimensions of the rectangle by using a system of equations.

length of a rectangle is 5 inches more than double its width means:

l=2w+5
the perimeter is 70 inches means:
2l+2w=70
or l+w=35
subbing in for l and simplifying...
(2w+5)+w=35
3w=30
so w=10
then that means
l+10=35
and so l=25
the dimensions must be: 25 inches x 10 inches

The length and width of a rectangle are consecutive even integers. The perimeter is 44 meters. Find the length and width.

2(l+w)=P
2(l+l+2)=44
2l+2=22
2l=20
l=10
length:10, width:12