Perimeter, Area & Volume — Quiz 6

Questions in this quiz (10)

1. In the following figure, the area of the shaded region is 20% of the area of the circle. If the radius of the circle is 20, what is the arc length from P to Q?

   • $$8\pi$$
   • $$2\pi$$
   • $$20\pi$$
   • $$72\pi$$

2. The base of a pyramid has the same area as the base of the cylinder, and the cylinder is twice the height of the pyramid. What is the ratio of the volume of the pyramid to the volume of the cylinder?

   • $$\frac{2}{3}$$
   • $$\frac{1}{3}$$
   • $$\frac{3}{2}$$
   • $$\frac{1}{6}$$

3. A cube has an edge length of 20 inches. A solid sphere with a radius of 10 inches is inside the cube, such that the sphere touches the center of each face of the cube. To the nearest cubic inch, what is the volume of the space in the cube not taken up by the sphere in cubic inches?

   • 3811.21
   • 4000.00
   • 4800.00
   • 4188.79

4. If the volume of a cube is $$y$$, what is the length of the longest diagonal of the cube in terms of $$y$$?

   • $$y^{1/3} \sqrt{3}$$
   • $$y^{1/3} \sqrt{2}$$
   • $$y^{1/3}$$
   • $$y^{2/3}$$

5. If all the water in a full pool with a length of 6 meters, a width of 4 meters, and a height of 3 meters is siphoned into an empty pool with a length of 10 meters and a width of 5 meters, how high will the top of the water be to the nearest centimeter?

   • 1.52
   • 144
   • 150
   • 1.44

6. If the ratio of the surface areas of two spheres is $$4 : 9$$, what is the ratio of their volumes?

   • $$8 : 27$$
   • $$4 : 9$$
   • $$16 : 81$$
   • $$2 : 3$$

7. The radius of a right circular cylinder is multiplied by a factor of 3, and its height is divided by a factor of 4. What is the ratio of the volume of the old cylinder to the volume of the new one?

   • $$3 : 4$$
   • $$16 : 81$$
   • $$4 : 9$$
   • $$16 : 27$$

8. What is the area, in square units, of the square inscribed in the circle given by the equation:$$(x+3)^2 + (y-5)^2 = 49?$$

   • $$7\sqrt{2}$$
   • 14
   • 49
   • 98

9. What is the area of the largest rhombus that can be inscribed in the ellipse given by the equation:$$\frac{x^2}{16} + \frac{y^2}{25} = 1?$$

   • 10
   • 40
   • 5
   • 8

10. If a cube with side length 3 is inscribed in a sphere, what is the surface area of the sphere? (The surface area of a sphere is $$4\pi r^2$$.)

    • $$\frac{3\sqrt{3}}{2}\pi$$
    • $$\frac{3}{2} \pi$$
    • $$4\pi$$
    • $$27\pi$$