Geometry and Trigonometry - Area and volume — Quiz 5

Questions in this quiz (10)

1. The three points shown define a circle. The circumference of this circle is $$k\pi$$, where $$k$$ is a constant. What is the value of $$k$$?

   • $$3$$
   • $$6$$
   • $$7$$
   • $$9$$

2. In the $$xy$$-plane shown, square $$ABCD$$ has its diagonals on the $$x$$- and $$y$$-axes. What is the area, in square units, of the square?

   • $$20$$
   • $$25$$
   • $$50$$
   • $$100$$

3. A right square prism has a height of $$12$$ units. The volume of the prism is $$1728$$ cubic units. What is the length, in units, of an edge of the base?

   • 12

4. Two identical rectangular prisms each have a height of $$60$$ centimeters. The base of each prism is a square, and the surface area of each prism is $$K$$ $$cm^2$$. If the prisms are glued together along a square base, the resulting prism has a surface area of $$\frac{47}{49}K$$ $$cm^2$$. What is the side length, in centimeters, of each square base?

   • $$5$$
   • $$7$$
   • $$10$$
   • $$14$$

5. What is the length of one side of a square that has the same area as a circle with radius $$3$$?

   • $$3$$
   • $$\sqrt{3\pi}$$
   • $$3\sqrt{\pi}$$
   • $$9\pi$$

6. A triangle has a base length of $$16$$ centimeters and a corresponding height of $$25$$ centimeters. What is the area, in square centimeters, of the triangle?

   • $$200$$
   • $$300$$
   • $$400$$
   • $$500$$

7. The dimensions of a right rectangular prism are $$3$$ inches by $$7$$ inches by $$10$$ inches. What is the surface area, in square inches, of the prism?

   • $$120$$
   • $$182$$
   • $$242$$
   • $$280$$

8. The length of the edge of the base of a right square prism is $$5$$ units. The volume of the prism is $$1000$$ cubic units. What is the height, in units, of the prism?

   • $$20$$
   • $$25$$
   • $$40$$
   • $$50$$

9. A right circular cylinder has a volume of $$72\pi$$. If the height of the cylinder is $$8$$, what is the radius of the cylinder?

   • $$2$$
   • $$3$$
   • $$4$$
   • $$6$$

10. Circle $$M$$ has a radius of $$6$$ millimeters. Circle $$N$$ has an area of $$64\pi$$ $$mm^2$$. What is the total area, in $$mm^2$$, of circles $$M$$ and $$N$$?

    • $$100\pi$$
    • $$120\pi$$
    • $$136\pi$$
    • $$144\pi$$