Area & Volume 2 — Geometry and Trigonometry

Questions in this quiz (10)

1. The surface area of a cube is $$96$$ square centimeters. What is the volume, in cubic centimeters, of the cube?

   • $$16$$
   • $$32$$
   • $$64$$
   • $$128$$

2. A cubic container is open at the top. The length of each of its edges is $$24$$ feet. What is the exterior surface area, in square feet, of the container?

   • $$2,304$$
   • $$2,880$$
   • $$3,456$$
   • $$4,608$$

3. A cylindrical tank with a radius of $$3$$ feet is partially filled with water. A solid cone with a radius of $$1.5$$ feet is placed in the tank until it is completely submerged. When the cone is submerged, the water level in the tank rises by $$2$$ feet. What is the height of the cone, in feet?

   • $$6$$
   • $$12$$
   • $$18$$
   • $$24$$

4. In the $$xy$$-plane, square $$PQRS$$ has its diagonals on the $$x$$- and $$y$$-axes. If vertex $$P$$ is located at $$(0,-7)$$, what is the area, in square units, of the square?

   • $$98$$
   • $$196$$
   • $$49$$
   • $$28$$

5. A sphere has a radius of $$5$$ feet. What is the volume, in cubic feet, of the sphere?

   • $$\frac{500\pi}{3}$$
   • $$\frac{1000\pi}{3}$$
   • $$\frac{250\pi}{3}$$
   • $$\frac{100\pi}{3}$$

6. A rectangular community garden has an area of $$2400$$ square meters. An architect creates a scale drawing of the garden. On the drawing, the length of each side is $$\frac{1}{8}$$ the length of the corresponding side of the actual garden. What is the area, in square meters, of the garden on the drawing?

   • $$25$$
   • $$37.5$$
   • $$75$$
   • $$300$$

7. A right rectangular prism has a square base. The volume of the prism is $$64$$ cubic units, and the length of a diagonal connecting opposite vertices of the prism is $$\sqrt{48}$$ units. The height of the prism, $$h$$, is an integer. What is the value of $$h$$?

   • $$2$$
   • $$4$$
   • $$8$$
   • $$16$$

8. A right triangle has sides of length $$3\sqrt{5}$$, $$4\sqrt{5}$$, and $$\sqrt{125}$$ units. What is the area of the triangle, in square units?

   • $$45$$
   • $$75$$
   • $$30$$
   • $$15$$

9. The table above shows the areas of rectangles $$C$$ and $$D$$ in square meters. Rectangle $$C$$ has a perimeter of $$40$$ meters. If both rectangles are similar, what is the perimeter, in meters, of rectangle $$D$$?

   • $$80$$
   • $$120$$
   • $$160$$
   • $$360$$

10. The figure shows a right circular cylinder with a radius of $$a$$ and a height of $$b$$. A second right circular cylinder has a volume that is $$108$$ times as large as the volume of the cylinder shown. Which of the following could represent the radius $$A$$, in terms of $$a$$, and the height $$B$$, in terms of $$b$$, of the second cylinder?

    • $$A=6a$$ and $$B=3b$$
    • $$A=9a$$ and $$B=4b$$
    • $$A=3a$$ and $$B=6b$$
    • $$A=4a$$ and $$B=12b$$