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
Answers
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.