The problem is asking for two things:

(i) To calculate the volume of the solid figure which is composed of two hemispheres and a cylinder.

(ii) To calculate the mass of a similar solid figure made of silver.

Let's solve this step by step:

(i) The volume of the solid is the sum of the volumes of the two hemispheres and the cylinder.

The volume of a sphere is given by the formula V = 4/3πr³. Since a hemisphere is half of a sphere, the volume of a hemisphere is V = 2/3πr³.

So, the volume of the large hemisphere is V = 2/3π(5.4)³ = 328.72 cm³.

The volume of the small hemisphere is V = 2/3π(3.6)³ = 97.43 cm³.

The volume of a cylinder is given by the formula V = πr²h. So, the volume of the cylinder is V = π(3.6)²(6.5) = 265.73 cm³.

Adding these volumes together, we get the total volume of the solid: 328.72 cm³ + 97.43 cm³ + 265.73 cm³ = 691.88 cm³. Rounded to the nearest cubic centimeter, this is 692 cm³.

(ii) The solid is mathematically similar to the original, so all lengths are scaled by the same factor. The radius of the cylinder in the silver solid is 0.6 cm, so the scale factor is 0.6 / 3.6 = 1/6.

The volume of a similar figure is scaled by the cube of the scale factor, so the volume of the silver solid is (1/6)³ = 1/216 of the volume of the original solid.

So, the volume of the silver solid is 692 cm³ / 216 = 3.20 cm³.

The problem states that 1 cm³ of silver has a mass of 10.49 grams. So, the mass of the silver solid is 3.20 cm³ * 10.49 g/cm³ = 33.57 g.

Question

The problem is asking for two things:

(i) To calculate the volume of the solid figure which is composed of two hemispheres and a cylinder.

(ii) To calculate the mass of a similar solid figure made of silver.

Let's solve this step by step:

(i) The volume of the solid is the sum of the volumes of the two hemispheres and the cylinder.

The volume of a sphere is given by the formula V = 4/3πr³. Since a hemisphere is half of a sphere, the volume of a hemisphere is V = 2/3πr³.

So, the volume of the large hemisphere is V = 2/3π(5.4)³ = 328.72 cm³.

The volume of the small hemisphere is V = 2/3π(3.6)³ = 97.43 cm³.

The volume of a cylinder is given by the formula V = πr²h. So, the volume of the cylinder is V = π(3.6)²(6.5) = 265.73 cm³.

Adding these volumes together, we get the total volume of the solid: 328.72 cm³ + 97.43 cm³ + 265.73 cm³ = 691.88 cm³. Rounded to the nearest cubic centimeter, this is 692 cm³.

(ii) The solid is mathematically similar to the original, so all lengths are scaled by the same factor. The radius of the cylinder in the silver solid is 0.6 cm, so the scale factor is 0.6 / 3.6 = 1/6.

The volume of a similar figure is scaled by the cube of the scale factor, so the volume of the silver solid is (1/6)³ = 1/216 of the volume of the original solid.

So, the volume of the silver solid is 692 cm³ / 216 = 3.20 cm³.

The problem states that 1 cm³ of silver has a mass of 10.49 grams. So, the mass of the silver solid is 3.20 cm³ * 10.49 g/cm³ = 33.57 g.

Knowee AI · Accepted Answer