Question

a piece of cake is cut in the shape of a sector of a circle of radius 7 cm. The thickness of the piece of cake in 9 cm. Find the curved surface area and the volume of the piece of the cake

Answer 1

Answer:

calculations based on the angle of 72°

Curved surface area = 79.1784 cm²

Volume  = 277.1244

Step-by-step explanation:

a) To calculate the curved surface are we need to find the length of the arc formed by the sector:

Finding the length of the arc or the perimeter of a sector requires that you have the angle formed by the sector. ( Since it is not provided in your question we can use a random value of 72° for the purpose of practice).

    Formula of calculating the length the arc of a sector:

        Ф/360° × 2πr

        Formula for the curved surface area:

                  Ф/360° × 2πrh

Where Ф is the angle formed by the sector, r is the radius of the sector and h is the thickness of the piece of cake ( The height of the shape formed).

Curved surface area = 72°/360° × 2πrh

                          = 1/5 × 2 ×3.142 × 7cm  × 9cm

                         = 79.1784 cm²

b) Volume of the piece of cake:

To find the volume of the piece of cake ( the shape formed); we need to find the surface area of the sector multiplied by the thickness of the cake.

           Formula of the volume:

                       Ф/360° × πr²h

  Volume = 72°/360° × 3.142 × 7² × 9

               = 1/5 × 3.142 × 49 cm²× 9cm

               = 277.1244 cm³

Therefore the volume of the piece of cake is 277.1244cm³

Note: All the calculations in this question, are based on the sector having an angle of 72°, incase the angle in your question was different, just substitute 72° with that angle and get the values of the curved surface area and volume.