each region below is being rotated about the line l. for each region, identify the solid generated by the…
each region below is being rotated about the line l. for each region, identify the solid generated by the rotation.
Answer
Explanation:
Step1: Recall 3 - D solid generation rules
Rotating a rectangle about an axis parallel to one of its sides generates a cylinder.
Step2: Analyze region (a)
Region (a) is a rectangle. When rotated about the line (l), it generates a cylinder.
Step3: Recall cone - generation rule
Rotating a right - angled triangle about one of its legs generates a cone.
Step4: Analyze region (b)
Region (b) is a right - angled triangle. When rotated about the line (l), it generates a cone.
Step5: Recall sphere - generation rule
Rotating a semi - circle about its diameter generates a sphere.
Step6: Analyze region (c)
Region (c) is a semi - circle. When rotated about the line (l) (which is its diameter), it generates a sphere.
Answer:
(a) Cylinder (b) Cone (c) Sphere