The ratio of the diameter and height of a cylinder is 4 : 5. Find the height of the cylinder, if its volume is 540π cubic units.

Identify the parallel lines and perpendicular lines from the given set.
2x + y = 1
9x + 3y = 6
y = 3x
y = -3x
2y = 4x +6
Y = - x/2

Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.
Carrie redesigned the container because the initial sketch did not account for cushioning material between the glasses. The area of the base of the newly designed container is   greater than the area of the base in the initial sketch. What is the area, in square inches, of the base of the newly designed container?

Note:
There is a shorter way of doing this problem. There is a simple rule followed while increasing or decreasing a value by a certain percentage.  When we decrease a quantity by x%, we multiply the quantity by (1-0.x). Whereas when we increase a quantity by x%, we multiply it with (1+0.x).

Find the equation of line that passes through the point (2, -9) and which is perpendicular to the line x = 5.

Use the perpendicular line formula to determine whether two given lines are perpendicular. For example, when the slope of two lines is given to compare, we can use the perpendicular line's formula. A 90-degree angle is created by two lines that are perpendicular to one another.
Slope exists on every line. Because it shows how quickly our line is rising or falling, the slope of a line reveals how steep a line is. Mathematically, the slope of a line is known as the ratio of change in the line's y-value to the change in its x-value.
¶A line's slope can be determined using its two points (x₁, y₁) and (x₂, y₂). The formula (y₂ - y₁) / is used to find the change in y and divided by the change in x. (x₂ - x₁).

Write the equations of the given lines.
Line 1: y-intercept = 3, slope = 2
Line 2: y-intercept = - 1, slope = -5

Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.
If the length and width of the container base in the initial sketch were doubled, at most how many more glasses could the new container hold?

Note:
A few simple ideas are used in solving this problem, like, area of a rectangle is given by the product of its length and breadth and the basic idea of division.

Identify a line having zero slope

Find the area of triangle with base 5 cm and whose height is equal to that of the rectangle with base 5 cm and area 20 cm²

A cuboid box has a square base of side 7 units and a height of 12 units. What is the cylinder with the maximum volume, which can be carved out of this cuboid?

Calculate the area and height of equilateral triangle whose perimeter is 48 cm

Identify a line with an undefined slope.

Write an equation of the line with undefined slope and passing through (5,11).

Find the :
a. Area of triangle whose three sides are 8 cm, 15 cm, 17 cm long
b .Find the altitude from opposite vertex to the side whose length is 15cm

An arc of a circle measures 2.4 radians. To the nearest degree, what is the measure, in degrees, of this arc? (Disregard the degree sign when gridding your answer.)

Note:
Another answer for this problem could be taken as 137 as well.
Unitary method is finding out the value of one unit from the relation given and then multiplies the value of the single unit with the number of required units.

The pillars in a house are in a cylindrical shape. Calculate the amount of concrete required to build up 21 such pillars with radius and height as 20 cm and 10 m respectively.

Find the area of triangle whose base is 10 cm and height is 5 cm