Question

Dona paints ornaments for a school play. Each ornament is as shown and is made up of two identical cones. She uses one bottle of paint to paint 196 in.2. How many bottles of paint does she need in order to paint 60 ornaments? Use 3.14 for pi.

Answer 1

The Total surface area of single cone can be determined as,

$\begin{gathered} \text{TSA}=\pi r^2+\pi rl \\ =3.14(2.6)^2+3.14(2.6)(10.2) \\ =21.2264in^2+83.2728in^2 \\ =104.4992in^2 \end{gathered}$

The total surface area of one ornament will be,

$\begin{gathered} \text{TSA}=2\times104.4992 \\ =208.9984in^2 \end{gathered}$

The total surface area of 60 ornaments will be,

$\begin{gathered} \text{TSA}=60\times208.9984in^2 \\ =12539.904in^2 \end{gathered}$

The number of bottles can be determined as,

$\begin{gathered} N=\frac{12539.904}{196} \\ =63.97 \\ \approx64 \end{gathered}$

Thus, the required number of bottles is 64.