Lamp shade

A lamp shade is in the form of a frustum of a cone with slant height 7 in., radii of bases 3 in. and 7 in. respectively. How much material is used in its construction if ¼ in. is allowed for the seam.

Correct answer:

S =  227.8 in²

Step-by-step explanation:

$$\begin{gathered} s=7\text{in} \\ {r}_1=3\text{in} \\ {r}_2=7\text{in} \\ {s}_2=s+\frac{1}{4}=7+\frac{1}{4}=\frac{7\cdot 4}{4}+\frac{1}{4}=\frac{28}{4}+\frac{1}{4}=\frac{28+1}{4}=\frac{29}{4}=7.25\text{in} \\ S=\pi \cdot (r_1+r_2)\cdot s_2=3.1416\cdot (3+7)\cdot 7.25=227.8{\text{in}}^2 \end{gathered}$$

Try another example