Question

What is the ratio of the surface areas from large to small

Answer 1

Given:

The length of the large cuboid is 63 km.

The breadth of the large cuboid is 63 km.

The height of the large cuboid is 42 km.

The length of the small cuboid is 36 km.

The breadth of the small cuboid is 36 km.

The height of the small cuboid is 24 km.

Required:

The ratio of surface areas from large to small.

Surface area of large cuboid is:

`\begin{gathered} Surface\text{ area = 2\lparen L}* B+B* H+H* L) \\ =2(42*63+63*63+63*42) \\ =2(2646+3969+2646) \\ =18522 \end{gathered}`

Surface area of small cuboid is:

`\begin{gathered} Surface\text{ area = 2\lparen L}* B+B* H+H* L) \\ =2(24*36+36*36+36*24) \\ =2(864+1296+864) \\ =6048 \end{gathered}`

The ratio of surface area is:

`\begin{gathered} Ratio=\frac{surface\text{ area of larger cuboid}}{surface\text{ area of smaller cuboid}} \\ =(18522)/(6048) \\ =(49)/(16) \end{gathered}`

Hence, the ratio of the surface area is 49: 16.