Question

6. ACT/SAT Tara has a cylindrical candle mold that is 8 inches high with a diameter of

Answer 1

48 (option B) votive candles are needed to fill the candle mold, If she would like to melt votive candles and reuse the wax.

Step-by-step explanation:

The given is,

              Cylindrical candle mold that is 8 inches high with a diameter of  3 inches.

               Votive  candle is a sylinder with a height or 1.5 inches and a radius of 0.5 inch.

Step: 1

               Formula to calculate the volume of cylinder,

                        $Volume, V = \pi r^{2} h$.................................(1)

               Where, r - Radius of cylinder

                           h - Height of cylinder

                           $\pi = 3.1415$

Step: 2

              For the Candle mold,

                         Diameter, D = 3 inches

                              Radius, r = $\frac{d}{2}$

                                              = $\frac{3}{2}$ = 1.5

                                            r = 1.5 inches

              Equation (1) becomes,

                        $V_{Candle mold} = \pi (1.5)^{2} (8)$

                                           = (3.1415)(2.25)(8)

                                           = 56.547 cubic inches

Step: 3

             For the Votive candle,

                                            r = 0.5 inches

                                           h = 1.5 inches

              Equation (1) becomes,

                        $V_{Candle mold} = \pi (0.5)^{2} (1.5)$

                                           = (3.1415)(0.25)(1.5)

                                           = 1.1780625 cubic inches

Step: 4

            No. of votive candles are needed to fill the candle mold,

                                                     =  $\frac{Volume_{candle mold} }{Volume _{Votive candles} }$

                                                     = $\frac{56.547}{1.1780625}$

                                                     = 48

             No. of votive candles are needed to fill the candle mold = 48

Result:

            48 (option B) votive candles are needed to fill the candle mold, If she would like to melt votive candles and reuse the wax.