Question

Two similar cuboids have corresponding widths of 11cm and 9cm.

a) Find the ratio of their surface areas.
b) If the surface area of the larger cuboid is 363 cm², find the surface area of the smaller cuboid.

a. ( frac(121)(81) ), 297 cm²
b. ( frac(9)(11) ), 198 cm²
c. ( frac(121)(81) ), 198 cm²
d. ( frac(9)(11) ), 297 cm²

Answer 1

To find the ratio of the surface areas, square the ratio of the widths. To find the surface area of the smaller cuboid, set up a proportion with the ratio of the widths.

Step-by-step explanation:

To find the ratio of the surface areas of the two similar cuboids, we need to compare their corresponding sides. The ratio of the widths is given as 11cm to 9cm. Since surface area is proportional to the square of the side length, we can square the ratio of the widths to find the ratio of the surface areas.

The ratio of the surface areas is (11/9)^2 = 121/81.

To find the surface area of the smaller cuboid, we can set up a proportion using the ratio of the widths. Let x be the surface area of the smaller cuboid. We can set up the equation (11/9)^2 = 363/x and solve for x.

The surface area of the smaller cuboid is 198 cm².