Jawab:

Penjelasan dengan langkah-langkah:

a. To find the volume of the composite solid, we need to find the volumes of the cylinder and the hemisphere and add them together.

The volume of the cylinder is given by:

V_cylinder = πr^2h

where r is the radius (half of the diameter) and h is the height.

Here, the diameter is 6x, so the radius is 3x.

The height is 5x.

V_cylinder = π(3x)^2(5x)

V_cylinder = 45πx^3

The volume of the hemisphere is given by:

V_hemisphere = (2/3)πr^3

where r is the radius.

Here, the radius is 6x.

V_hemisphere = (2/3)π(6x)^3

V_hemisphere = 288πx^3

The total volume of the composite solid is:

V_total = V_cylinder + V_hemisphere

V_total = 45πx^3 + 288πx^3

V_total = 333πx^3

Therefore, the volume of the composite solid is 333πx^3.

b. To find the total external surface area of the composite solid, we need to find the surface area of the cylinder and the surface area of the hemisphere (excluding the flat base that rests on the cylinder), and add them together.

The surface area of the cylinder is given by:

A_cylinder = 2πrh + 2πr^2

where r is the radius and h is the height.

Here, the radius is 3x and the height is 5x.

A_cylinder = 2π(3x)(5x) + 2π(3x)^2

A_cylinder = 30πx^2 + 18πx^2

A_cylinder = 48πx^2

The surface area of the hemisphere (excluding the base) is half the surface area of a sphere with the same radius:

A_hemisphere = (1/2) × 4πr^2

A_hemisphere = (1/2) × 4π(6x)^2

A_hemisphere = 72πx^2

The total external surface area of the composite solid is:

A_total = A_cylinder + A_hemisphere

A_total = 48πx^2 + 72πx^2

A_total = 120πx^2

Therefore, the total external surface area of the composite solid is 120πx^2.