The toroid formed by rotating the rectangular figure gives;
a. A toroid
b. 374•π
c. 400•π
d. The surface area will be 4 times the initial surface area
The volume will be 8 times the initial volume
How can the shape formed and it's characteristics be found?
Taking the distance from the y-axis as 8
Width of the rectangle; 2.5
Length; 6
We have;
a. The solid of revolution is a toroid, having sharp corner edges
b. The surface area is found using the surface area of a hollow cylinder as follows;
Outer radius = 8 + 6 = 14
Inside radius = 8
Width = 2.5
Outer area = 2• π × 14 × 2.5 = 70•π
Inner area = 2• π × 8 × 2.5 = 40•π
[tex]{\pi \cdot 14 }^{2} - {\pi \cdot 8 }^{2} = 132 \cdot\pi[/tex]
The surface area of the figure is therefore;
- 70•π + 40•π + 2×132•π = 374•π
c. The volume of the solid of revolution is found as follows;
[tex]{\pi \cdot 14 }^{2} \times 2.5 - {\pi \cdot 8 }^{2} \times 2.5= 400 \cdot \pi[/tex]
- The volume of solid is 400•π
e. When the dimensions are doubled, we have;
The linear scale factor = 2
The area scale factor = 2^2 = 4
Therefore;
- The surface area of the solid, S' = 4 × 374•π = 1496•π (4 times initial surface area)
The volume scale factor = 2^3 = 8
The volume of the solid following the enlargement, is therefore;
Learn more about scale factor s here:
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