Question

A rock is in the shape of a sphere with a radius of 5.08 centimeters. The rock has a density of 5.5 grams per cubic centimeter. Find the mass of the rock to the nearest whole gram.

Answer 1

The mass of the rock is 3020.27 grams , if a rock is in the shape of a sphere with a radius of 5.08 centimeters and the rock has a density of 5.5 grams per cubic centimeter,

Step-by-step explanation:

The given is,

            Radius of the rock is 5.08 cm (Sphere)

            Density of rock 5.5 grams per cubic centimeters

Step:1

           Formula for volume of sphere,

                               $Volume, V= \frac{4}{3} \pi r^{3}$..........................(1)

          Where, r - Radius of sphere

          From the given values,

                          r = 5.08 cm

          Equation (1) becomes,

                                    $V= \frac{4}{3} \pi (5.08)^{3}$

                                    $V= \frac{4}{3} (3.1415) (5.08)^{3}$

                                        $= \frac{4}{3} (3.1415) (131.097)$

                                    V = 549.14 cubic centimeters

Step:2

          Mass of rock = Volume of rock × Density of rock

                                = 549.14 × 5.5          ( ∵ $cm^{3} (\frac{ gram}{cm^{3}} ) = gram$ )

                                = 3020.27 grams

  Mass of the rock = 3020.27 grams

Result:

      The mass of the rock is 3020.27 grams , if a rock is in the shape of a sphere with a radius of 5.08 centimeters and the rock has a density of 5.5 grams per cubic centimeter,