Grade 8 Geometry Problems and Questions with Answers

Geometry problems and questions with answers for grade 8 are presented. These problems and questions deal with calculating angles, perimeters, areas and volumes. Questions on similarity and reflection are also included. Also solutions and explanations are included.

1. Find the total surface area and the volume of a closed cylindrical container with radius 5 cm and a height of 34 cm.

   Hint \[ \text{Formulas:} \qquad A = 2\pi r^2 + 2\pi rh, \quad V = \pi r^2 h\]

2. Find the total surface area and the volume of a closed conical container with radius 5 cm and a height of 15 cm (round your answer to the nearest unit).

   Hint \[ \text{Formulas:} \qquad A = \pi r^2 + \pi r\sqrt{r^2 + h^2}, \qquad V = \frac{1}{3}\pi r^2 h\]

3. A cube has a total surface area of the six faces equal to 150 square feet. What is the volume of the cube?

   Hint \[ \text{Formulas:} \qquad A = 6s^2, \qquad V = s^3, \quad \text{s is the side}\]

4. Which two angles are complementary?
   1. 21 \(^{\circ} \) and 78 \(^{\circ} \)
   2. 58 \(^{\circ} \) and 22 \(^{\circ} \)
   3. 67 \(^{\circ} \) and 23 \(^{\circ} \)
   4. 140 \(^{\circ} \) and 40 \(^{\circ} \)

   Hint\[ \text{Definition:} \qquad \text{Complementary angles: } \alpha + \beta = 90^\circ\]

5. Which two angles are not supplementary?
   1. 30 \(^{\circ} \) and 150 \(^{\circ} \)
   2. 5 \(^{\circ} \) and 175 \(^{\circ} \)
   3. 89 \(^{\circ} \) and 91 \(^{\circ} \)
   4. 23 \(^{\circ} \) and 177 \(^{\circ} \)

   Hint\[ \text{Definition:} \qquad \text{Supplementary angles: } \alpha + \beta = 180^\circ\]

6. Find the height h of the trapezoid so that its area is equal to 400 square cm.

   Hint\[ \text{Formulas:} \qquad A_{trapezoid} = \frac{1}{2}h(b_1 + b_2)\]

7. Find the width w of the parallelogram so that its area is equal to 600 square feet.

   Hint\[ \text{Formulas:} \qquad A_{parallelogram} = b \times h\]

8. Find area of the shaded shape.
9. Find the total surface area of the box open at the top.
10. If the quadrilateral ABCD is a parallelogram, what are the coordinates of point D?
11. Which of these are right triangles?

    Hint\[ \text{In a right triangle:} \quad a^2 + b^2 = c^2 \; \text{(Pythagora)} \quad \text{and the size of one of the angles is} \; 90^{\circ} \]

12. Find x if triangle ABC is a right triangle with angle B = 90\(^{\circ} \)

    Hint\[\text{In a triangle: } \angle A + \angle B + \angle C = 180^\circ\]

13. Find all the unknown sides x, y, z and w if all three triangles are similar.

    Hint\[ \text{When two triangles are similar, their corresponding sides are proportional:} \quad \frac{a}{a'} = \frac{b}{b'} = \frac{c}{c'}\]

14. A quadrilateral with vertices (-2,6), (6,8), (9,2) and (4,-1) is reflected on the x-axis. What are the coordinates of the vertices of the quadrilateral after reflection?

    Hint\[Reflection\ over\ x\text{-}axis: (x,y) \to (x,-y)\]

15. The side of cube A is 3 times the side of cube B. The volume of cube A is 3,375 cubic feet. Find the volume of cube B.

    Hint\[ \text{Formulas:} \qquad V = s^3 \]

16. The length of rectangle A is 24 cm and the length of rectangle B is 96 cm. The two rectangles are similar. Find the ratio of the area of A to the area of B.

    HintThe corresponding sides of two similar rectangle are proprtional.

More References and Links

• Middle School Math (Grades 6, 7, 8, 9) - Free Questions and Problems With Answers
• High School Math (Grades 10, 11 and 12) - Free Questions and Problems With Answers
• Primary Math (Grades 4 and 5) with Free Questions and Problems With Answers