An antique vase sells for $80. If the price increases by 18%, and then decreases by 20%, what is the new price?

$113.28

Step-by-step explanation:

18% of 80 = 14.40

80 + 14.40 = 94.40

20% of 94.40 = 18.88

94.40 + 18.88 = 113.28

around 292,000 cm³

Step-by-step explanation:

The volume of the truncated pyramid is the same as taking the large pyramid MINUS the smaller pyramid on top.

The volume of a pyramid can be found using the following expression:

l = the length of the base

w = the width of the base

h = the height of the pyramid

Let's calculate the volume of the larger pyramid:

The length and width of the base are 100 cm, and the height is also 100 cm (50cm + 50cm).

Let's keep it like that for now.

Now, the smaller pyramid is a bit less obvious. The height is given, but the length/width of the base isn't as obvious. Now, we need to use one important fact. The smaller pyramid is similar to the larger pyramid. It has the same shape as the larger pyramid, it's just scaled down.

We know the scaling, since we know the height of both the larger and smaller pyramid.

Height of the small pyramid: 50cm

Height of the large pyramid: 100cm

The smaller pyramid is scaled down by a factor of 1/2 on all sides.

Thus, we know that the base/length of the smaller pyramid must be half of the larger pyramid. Since the base/length of the large pyramid was 100cm..

..the smaller pyramid has a base/length of 50 cm.

Now, let's use the same expression as above:

Now, let's subtract the smaller pyramid's volume from the large pyramid's volume:

875000 / 3 ≈ 292000

around 292,000 cm³