Rotations With Dimensions

Which three-dimensional object below is generated by the rotation of a rectangle?

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If the rectangle above is continuously rotated about side w, which solid figure is formed?

• pyramid

• rectangular prism

• cone

• cylinder

Which object is formed when right triangle RST shown above is rotated around leg RS?

• a pyramid with a square base

• an isosceles triangle

• a right triangle

• a cone

Triangle ABC represents a metal flag on pole AD. On a windy day the triangle spins around the pole so fast that it looks like a three-dimensional shape. Which shape would the spinning flag create?

• sphere

• pyramid

• right circular cylinder

• cone

If an equilateral triangle is continuously rotated around one of its medians, which 3-dimensional object is generated?

• cone

• pyramid

• prism

• sphere

Circle O is centered at the origin. In the diagram below, a quarter of circle O is graphed. Which 3-dimensional figure is generated when the quarter circle is continuously rotated about the y-axis?

• cone

• sphere

• cylinder

• hemisphere

An isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object. The three-dimensional object is a

• cylinder with a diameter of 6

• cylinder with a diameter of 12

• cone with a diameter of 6

• cone with a diameter of 12

Right triangle ABC has legs whose lengths are 4 and 6. What is the volume of the three-dimensional object formed by continuously rotating the right triangle around AB ?

• 32π

• 48π

• 96π

• 144π

A rectangle whose length and width are 10 and 6, respectively, is shown. The rectangle is continuously rotated around a straight line to form an object whose volume is 150π.

• a long side

• a short side

• the vertical line of symmetry

• the horizontal line of symmetry

Triangle ABC, with vertices at A(0,0), B(3,5), C(0,5) and , is graphed. Which figure is formed when ΔABC is rotated continuously about BC?

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