Calculate the volumes of the hollow cylinder and hollow sphere as shown below in figures (a) and (b).Calculate the areas of the sheets metal panels shown in the figures (a) (b) below. Make a list of the data you will use to do this.

2022 – 2023
Scenario
Mensuration is the branch of mathematics dealing with measurements of area and volume. In engineering, it is used when we have to calculate the area of a metal sheet required for a product, or the volume of a storage tank or a boiler etc. On the other hand, trigonometry is the study of the relationship between the sides and angles of
triangles. It is used to find missing dimensions that we may need to calculate areas and volumes. Your department supervisor wants you prove your ability at mensuration and trigonometry and he has asked to solve all the tasks in this assignment.
Task 1 [P4]
Calculate the area of hollowed rectangle and ring shown below in figures (a) and (b).
Task 2 [P5]
Calculate the volumes of the hollow cylinder and hollow sphere as shown below in figures (a) and (b).
2022 – 2023
Task 3 [P6]
Solve the angles and side dimensions for each of the triangles shown below. Your calculations must use where appropriate of Pythagoras’ theorem and sine, cosine, and tangent functions.
Task 4 [M2]
Calculate the areas of the sheets metal panels shown in the figures (a) (b) below. Make a list of the data you will use to do this.
2022 – 2023
Task 5 [M3]
Calculate the volumes of the spherical pressure vessel and the conical hopper as shown in the figures (a) and (b)
below. Make a list of the data you are going to use to do this.
2022 – 2023
Task 6 [M4]
Calculate the height, sloping side lengths and angles of the trapezoid shaped roof truss as shown in figure (a) below.
Calculate the angles and side dimensions of the triangle as shown in the figure (b) below.
(a) (b)

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