Question

Two tins are geometrically similar. If the ratio of their volumes is 27:64, find the ratio of their curved surface area.

Answer 1

volume are in the ratio 27:64

curved surface area in the ratio

9:16

Answer 2

Answer:

The ratio of their curved surface area is 9:16.

Step-by-step explanation:

We are given that two tins are geometrically similar

The ratio of their volumes =$\frac{27}[64}$

Let $L_1, B_1 H_1$ are the dimensions of one tin and $L_2,B_2,H_2$ are the dimensions of second tin.

We know that tin is cuboid in shape

Therefore, Volume of cuboid=$Length\times breadth\times height$

Volume of one tin=$L_1B_1H_1$

Volume of second tine=$L_2B_2H_2$

The ratio of two tine volume

$\frac{Volume \;of \;one t\;ine}{Volume\;of\;second\;tin}=\frac{L_1B_1H_1}{L_2B_2H_2}=\frac{27}{64}$

We know that when two tin are similar then the ratio of corresponding sides are equal in proportions

$\frac{L_1}{L_2}=\frac{B_1}{B_2}=\frac{H_1}{H_2}$

Therefore, we can write

$(\frac{L_1}{L_2})^3=\frac{27}{64}=(\frac{3}{4})^3$

$\frac{L_1}{L_2}=\frac{3}{4}$

We know that when base on both sides are equal then the value of power should be equal.

$\frac{L_1}{L_2}=\frac{B_1}{B_2}=\frac{H_1}{H_2}=\frac{3}{4}$

$L_1=B_1=H_1=3 x$

$L_2=B_2=H_2=4 x$

Hence, the two tins are cubes in shape because all sides of are equal of each tin.

Curved surface area of cube=$6a^2$

Therefore,

$\frac{Curved\;surface\;area\;of\;one \;tin}{curved\;surface\;area\;of \;second\;tin}=\frac{6L_1^2}{6L_2^2}=(\frac{L_1}{L_2})^2=(\frac{3}{4})^2$

$\frac{Curved\;surface\;area\;of\;one \;tin}{curved\;surface\;area\;of \;second\;tin}=\frac{9}{16}$

Hence, the ratio of their curved surface area is 9:16.