TExES Core Mathematics Geometry Area and Volume Quiz

1. A rectangle has length 12 cm and width 8 cm. What is its area?

96 cm²

20 cm²

40 cm²

144 cm²

To find the area of a rectangle, multiply its length by its width. Here, the length is 12 cm and the width is 8 cm. Therefore, the area is calculated as 12 cm × 8 cm = 96 cm². This represents the total space within the rectangle.

Explanation

To find the area of a rectangle, multiply its length by its width. Here, the length is 12 cm and the width is 8 cm. Therefore, the area is calculated as 12 cm × 8 cm = 96 cm². This represents the total space within the rectangle.

2. A cylinder has radius 5 m and height 10 m. Which formula finds its volume?

V = πr²h

V = 2πrh

V = πr³

V = 4/3πr³

The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius and h is the height. This formula derives from the area of the circular base (πr²) multiplied by the height, effectively stacking the base area along the cylinder's height to find the total volume.

Explanation

The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius and h is the height. This formula derives from the area of the circular base (πr²) multiplied by the height, effectively stacking the base area along the cylinder's height to find the total volume.

3. A triangle has base 6 cm and height 9 cm. Calculate its area.

27 cm²

54 cm²

15 cm²

18 cm²

The area of a triangle is calculated using the formula: Area = (base × height) / 2. Here, substituting the given values, Area = (6 cm × 9 cm) / 2 = 54 cm² / 2 = 27 cm². Thus, the area of the triangle is 27 cm².

Explanation

The area of a triangle is calculated using the formula: Area = (base × height) / 2. Here, substituting the given values, Area = (6 cm × 9 cm) / 2 = 54 cm² / 2 = 27 cm². Thus, the area of the triangle is 27 cm².

4. A cube has side length 4 inches. What is its volume?

16 in³

64 in³

48 in³

256 in³

The volume of a cube is calculated using the formula V = side length³. For a cube with a side length of 4 inches, the calculation is 4³ = 4 × 4 × 4 = 64 cubic inches. Thus, the volume of the cube is 64 in³.

Explanation

The volume of a cube is calculated using the formula V = side length³. For a cube with a side length of 4 inches, the calculation is 4³ = 4 × 4 × 4 = 64 cubic inches. Thus, the volume of the cube is 64 in³.

5. A circle has diameter 14 cm. Find its area (use π ≈ 3.14).

43.96 cm²

153.86 cm²

615.44 cm²

307.72 cm²

To find the area of a circle, use the formula A = πr². The radius r is half the diameter, so r = 14 cm / 2 = 7 cm. Plugging in the values, A = 3.14 × (7 cm)² = 3.14 × 49 cm² = 153.86 cm². Thus, the area of the circle is 153.86 cm².

Explanation

To find the area of a circle, use the formula A = πr². The radius r is half the diameter, so r = 14 cm / 2 = 7 cm. Plugging in the values, A = 3.14 × (7 cm)² = 3.14 × 49 cm² = 153.86 cm². Thus, the area of the circle is 153.86 cm².

6. A rectangular prism has length 5, width 3, and height 7. What is its volume?

105 cubic units

30 cubic units

210 cubic units

15 cubic units

To find the volume of a rectangular prism, multiply its length, width, and height. In this case, the volume is calculated as 5 (length) × 3 (width) × 7 (height) = 105 cubic units. Thus, the volume of the prism is 105 cubic units.

Explanation

To find the volume of a rectangular prism, multiply its length, width, and height. In this case, the volume is calculated as 5 (length) × 3 (width) × 7 (height) = 105 cubic units. Thus, the volume of the prism is 105 cubic units.

7. A sphere has radius 3 cm. Using V = 4/3πr³, what is its volume?

36π cm³

27π cm³

12π cm³

9π cm³

To find the volume of a sphere, use the formula V = 4/3πr³. With a radius (r) of 3 cm, calculate: V = 4/3π(3)³ = 4/3π(27) = 36π cm³. Thus, the volume of the sphere is 36π cm³.

Explanation

To find the volume of a sphere, use the formula V = 4/3πr³. With a radius (r) of 3 cm, calculate: V = 4/3π(3)³ = 4/3π(27) = 36π cm³. Thus, the volume of the sphere is 36π cm³.

8. The area of a square is 144 m². What is the length of one side?

12 m

36 m

72 m

288 m

To find the length of one side of a square, take the square root of its area. Since the area is 144 m², the calculation is √144 = 12 m. Thus, each side of the square measures 12 meters.

Explanation

To find the length of one side of a square, take the square root of its area. Since the area is 144 m², the calculation is √144 = 12 m. Thus, each side of the square measures 12 meters.

9. A trapezoid has parallel sides of 8 cm and 12 cm, with height 5 cm. Find its area.

40 cm²

50 cm²

100 cm²

60 cm²

To find the area of a trapezoid, use the formula: Area = (1/2) × (Base1 + Base2) × Height. Here, Base1 is 8 cm, Base2 is 12 cm, and the height is 5 cm. Plugging in these values, Area = (1/2) × (8 + 12) × 5 = (1/2) × 20 × 5 = 50 cm².

Explanation

To find the area of a trapezoid, use the formula: Area = (1/2) × (Base1 + Base2) × Height. Here, Base1 is 8 cm, Base2 is 12 cm, and the height is 5 cm. Plugging in these values, Area = (1/2) × (8 + 12) × 5 = (1/2) × 20 × 5 = 50 cm².

10. A cone has radius 4 in and height 9 in. Which volume formula applies?

V = πr²h

V = 1/3πr²h

V = 2/3πr²h

V = 4/3πr³

The volume of a cone is calculated using the formula V = 1/3πr²h, where r is the radius and h is the height. This formula accounts for the cone's tapering shape, indicating that its volume is one-third that of a cylinder with the same base and height.

Explanation

The volume of a cone is calculated using the formula V = 1/3πr²h, where r is the radius and h is the height. This formula accounts for the cone's tapering shape, indicating that its volume is one-third that of a cylinder with the same base and height.

11. The circumference of a circle is 20π cm. What is its radius?

5 cm

10 cm

20 cm

40 cm

The circumference of a circle is calculated using the formula \(C = 2\pi r\), where \(r\) is the radius. Given that the circumference is \(20\pi\) cm, we can set up the equation \(20\pi = 2\pi r\). Dividing both sides by \(2\pi\) gives \(r = 10\) cm.

Explanation

The circumference of a circle is calculated using the formula \(C = 2\pi r\), where \(r\) is the radius. Given that the circumference is \(20\pi\) cm, we can set up the equation \(20\pi = 2\pi r\). Dividing both sides by \(2\pi\) gives \(r = 10\) cm.

12. A rectangular prism has surface area formula SA = 2(lw + lh + wh). If l=3, w=4, h=5, what is the SA?

47 sq units

60 sq units

94 sq units

120 sq units

To find the surface area of the rectangular prism, substitute the dimensions into the formula: SA = 2(lw + lh + wh). Calculating each term: lw = 12, lh = 15, wh = 20. Adding these gives 47, and multiplying by 2 results in a surface area of 94 square units.

Explanation

To find the surface area of the rectangular prism, substitute the dimensions into the formula: SA = 2(lw + lh + wh). Calculating each term: lw = 12, lh = 15, wh = 20. Adding these gives 47, and multiplying by 2 results in a surface area of 94 square units.