Question

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?

Hint:

**Hint:**

We simply need to find the area of the new container where the area of the base is 25% greater than the previous design. First we find 25% of the area of the base of the previously designed container and then just add that value to the area of the previously designed container to find the area of the newly designed container.

## The correct answer is: 135

### Initial length of the base of the container = 12 inches

Initial breadth of the base of the container = 9 inches

Thus, initial area of the base of the container = square inches

= 108 square inches

According to the question, the new area of the base is 25% greater than the initial area of the base.

First we find the increase in the area of the base

25% of initial area is given by

The increase in the area of the base is by 27 square inches

Thus, the new area of the base = (108+27) square inches

= 135 square inches

= 135 square inches

Thus, the area of the base of the newly designed container = 135 sq.inches

**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).

### Related Questions to study

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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 (x_{1}, y_{1}) and (x_{2}, y_{2}). The formula (y_{2} - y_{1}) / is used to find the change in y and divided by the change in x. (x_{2} - x_{1}).

### 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 (x_{1}, y_{1}) and (x_{2}, y_{2}). The formula (y_{2} - y_{1}) / is used to find the change in y and divided by the change in x. (x_{2} - x_{1}).

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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.

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.

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### 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 cm^{2}

### 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?

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### 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

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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.

### 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.