The volume of two similar rectangular prisms are 64cm^3 and 1000cm^3. The surface area of the smaller figure is 112cm^2. What is the surface area in square centimeters of the

the scale ratio is 4:10 = 2:5, so the area ratio is 4:25.

112 * 25/4 = ?

bigger figure?

Well, if the smaller figure's surface area is 112cm^2, then the bigger figure's surface area must be... drumroll, please... Bigger! But how much bigger?

Let's do a little math magic to find out.

The ratio of the volumes of two similar figures is the cube of the ratio of their side lengths. In this case, the volume ratio is 1000cm^3 / 64cm^3, which simplifies to 15.625. So, the ratio of side lengths is the cube root of that, which is roughly 2.5.

Now, let's apply this ratio to the surface area of the smaller figure. Since the surface area is proportional to the square of the side lengths, we multiply the smaller surface area (112cm^2) by the square of the ratio (2.5 * 2.5), which is 6.25.

So, the surface area of the bigger figure is 112cm^2 * 6.25 = 700cm^2 (approximately).

And there you have it! The surface area of the bigger figure is approximately 700 square centimeters. Math and humor, working together like a clown and a balloon animal!

larger figure?

To find the surface area of the larger figure, we need to determine the scale factor between the two figures.

The scale factor can be found by taking the cube root of the ratio of their volumes:

Scale factor = (volume of larger figure)^(1/3) / (volume of smaller figure)^(1/3)

Scale factor = 1000^(1/3) / 64^(1/3)

Scale factor = 10 / 4

Scale factor = 2.5

Since the figures are similar, the side lengths of the larger figure are 2.5 times the side lengths of the smaller figure.

Therefore, to find the surface area of the larger figure, we can multiply the surface area of the smaller figure by the square of the scale factor.

Surface area of larger figure = (Surface area of smaller figure) * (scale factor)^2

Surface area of larger figure = 112 * 2.5^2

Surface area of larger figure = 112 * 6.25

Surface area of larger figure = 700 cm^2

Therefore, the surface area of the larger figure is 700 cm^2.

larger figure?

To find the surface area of the larger figure, we can use the concept of similarity. Similar figures have proportional sides, meaning that corresponding sides are in the same ratio.

Let's denote the length, width, and height of the smaller figure as l1, w1, and h1, respectively. Similarly, the length, width, and height of the larger figure will be l2, w2, and h2.

We are given:

Volume of the smaller figure = 64 cm^3,
Volume of the larger figure = 1000 cm^3,
Surface area of the smaller figure = 112 cm^2.

Since the volumes of similar figures are in the ratio of the cubes of their corresponding sides, we can write:

(l2 / l1) * (w2 / w1) * (h2 / h1) = (volume of the larger figure) / (volume of the smaller figure)

Substituting the given values:

(l2 / l1) * (w2 / w1) * (h2 / h1) = 1000 / 64

Simplifying, we find:

(l2 / l1) * (w2 / w1) * (h2 / h1) = 15.625

Since the figures are rectangular prisms, the surface area can be expressed as:

Surface area = 2lw + 2lh + 2wh

For the smaller figure, we have:

Surface area of the smaller figure = 2(l1w1 + l1h1 + w1h1) = 112 cm^2

For the larger figure, we need to find the new surface area:

Surface area of the larger figure = 2(l2w2 + l2h2 + w2h2)

Now, let's find the value of (l2w2 + l2h2 + w2h2).

By substituting the ratios we found earlier:

((l2 / l1) * (w2 / w1) * (h2 / h1)) * (l1w1 + l1h1 + w1h1) = (l2w2 + l2h2 + w2h2)

Substituting the known values:

15.625 * 112 = (l2w2 + l2h2 + w2h2)

Simplifying, we find:

l2w2 + l2h2 + w2h2 = 1750

Therefore, the surface area of the larger figure is 1750 square centimeters.