Area & Volume 1 — Geometry and Trigonometry

Questions in this quiz (12)

1. A triangle in the $$xy$$-plane has vertices at $$(2,2)$$, $$(7,4)$$, and $$(5,9)$$. What is the area, in square units, of this triangle?

   • $$9$$
   • $$11$$
   • $$13$$
   • $$15$$

2. A rectangular prism has a square base with side length $$8$$ inches and a height of $$15$$ inches. From this prism, a cube with side length $$4$$ inches is removed from one corner. Which expression represents the volume, in $$in^3$$, of the remaining solid?

   • $$8\cdot8\cdot4-15\cdot4\cdot4$$
   • $$8\cdot8\cdot15+4\cdot4$$
   • $$8\cdot8\cdot15-4\cdot4\cdot4$$
   • $$8\cdot8\cdot15-6\cdot4\cdot4$$

3. The line segment shown in the $$xy$$-plane represents one of the legs of a right triangle. The area of this triangle is $$10\sqrt{17}$$ square units. What is the length, in units, of the other leg of this triangle?

   • $$10$$
   • $$20$$
   • $$2\sqrt{17}$$
   • $$5$$

4. Cube $$A$$ has an edge length of $$3$$ inches. The volume of cube $$B$$ is $$27$$ times the volume of cube $$A$$. What is the length, in inches, of one edge of cube $$B$$?

   • $$18$$
   • $$27$$
   • $$9$$
   • $$12$$

5. The width of a rectangle is $$8$$ centimeters. The length of the rectangle is $$5$$ centimeters longer than the width. What is the area, in square centimeters, of this rectangle?

   • $$40$$
   • $$64$$
   • $$104$$
   • $$169$$

6. A large cylindrical water tank has a radius of $$5$$ feet and a height of $$18$$ feet. Water from the tank is used to completely fill small conical cups. Each cup has a radius of $$3$$ inches and a height of $$6$$ inches. What is the maximum number of cups that can be filled from the tank?Note: $$1$$ foot $$=$$ $$12$$ inches

   • $$86,400$$
   • $$43,200$$
   • $$144$$
   • $$72$$

7. A right circular cone has a radius of $$\frac{5}{2}$$ inches and a height of $$\frac{9}{2}$$ inches. What is the volume, in cubic inches, of the cone?

   • $$\frac{75\pi}{8}$$
   • $$\frac{75\pi}{4}$$
   • $$\frac{225\pi}{8}$$
   • $$\frac{225\pi}{4}$$

8. Square $$P$$ has a side length of $$12$$ centimeters. The perimeter of square $$Q$$ is $$4$$ times the perimeter of square $$P$$. What is the length, in centimeters, of one side of square $$Q$$?

   • $$12$$
   • $$24$$
   • $$36$$
   • $$48$$

9. The legs of a right triangle have lengths $$x$$ and $$x+4$$. If the triangle has an area of $$48$$ square units, what is the length of the smaller side?

   • $$6$$
   • $$8$$
   • $$10$$
   • $$12$$

10. A grain silo is designed in the shape of a cylinder with a hemisphere on top. The diameter of the silo is $$d$$ and the height of the cylindrical portion is $$2d$$. The silo can hold a maximum volume of $$3016$$ cubic meters. The volume of the entire silo is $$\frac{8\pi d^3}{3}$$. What is the value of $$d$$, in meters?

    • $$4.93$$
    • $$6.60$$
    • $$7.11$$
    • $$14.23$$

11. Rectangles JKLM and RSTU are similar. The length of each side of RSTU is $$5$$ times the length of the corresponding side of JKLM. The area of rectangle JKLM is $$18$$ square units. What is the area, in square units, of rectangle RSTU?

    • $$90$$
    • $$450$$
    • $$18$$
    • $$125$$

12. Two similar hexagons, ABCDEF and GHIJKL, are shown. Each side length of hexagon ABCDEF is $$4$$ times the corresponding side length of hexagon GHIJKL. The area of hexagon ABCDEF is $$256$$ square meters. What is the area, in square meters, of hexagon GHIJKL?

    • $$16$$
    • $$25$$
    • $$26$$
    • $$28$$