GED Math Area Perimeter and Volume of Shapes Quiz

The area of a rectangle is calculated by multiplying its length by its width. Here, the length is 12 cm and the width is 8 cm. Thus, the area is 12 cm × 8 cm = 96 cm².

To find the length of one side of a square, divide the perimeter by 4, since a square has four equal sides. Here, the perimeter is 36 inches, so 36 divided by 4 equals 9 inches, which is the length of one side.

To find the circumference of a circle, use the formula C = 2πr. Here, the radius (r) is 5 meters. Plugging in the values, C = 2 × 3.14 × 5 = 31.4 meters. Thus, the circumference of the circle is 31.4 meters.

The area of a triangle is calculated using the formula: Area = 1/2 × base × height. Substituting the given values, Area = 1/2 × 10 cm × 6 cm, which equals 30 cm². This confirms that the area of the triangle is indeed 30 cm².

To find the volume of a rectangular prism, multiply its length, width, and height. In this case, the volume is calculated as 4 m (length) × 3 m (width) × 5 m (height) = 60 m³. Thus, the volume of the prism is 60 cubic meters.

The volume of a cylinder is calculated using the formula V = πr²h. Substituting the given values, V = 3.14 × (3 cm)² × 10 cm. This simplifies to V = 3.14 × 9 cm² × 10 cm, which equals 282.6 cm³. Thus, the volume of the cylinder is 282.6 cm³.

To find the radius of a circle given its area, use the formula \( A = πr^2 \). Rearranging gives \( r = \sqrt{\frac{A}{π}} \). Substituting \( A = 50.24 \, cm² \) and \( π ≈ 3.14 \) results in \( r = \sqrt{\frac{50.24}{3.14}} \approx 4 \, cm \).

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 the values: Area = (1/2) × (8 + 12) × 5 = (1/2) × 20 × 5 = 50 cm².

To find the width of the rectangle, use the perimeter formula: P = 2(length + width). Given the perimeter (50 inches) and length (15 inches), the equation becomes 50 = 2(15 + width). Simplifying this gives 25 = 15 + width, leading to a width of 10 inches.

To find the volume of a sphere, use the formula \( V = \frac{4}{3} \pi r^3 \). Substituting the radius \( r = 6 \) cm and \( \pi \approx 3.14 \), we calculate \( V = \frac{4}{3} \times 3.14 \times 6^3 \), which equals 904.32 cm³.

To find the volume of a cone, use the formula \( V = \frac{1}{3} \pi r^2 h \). Substituting the given radius (4 cm) and height (9 cm) into the formula, we calculate \( V = \frac{1}{3} \times 3.14 \times (4^2) \times 9 \), which results in 150.72 cm³.

To find the perimeter of the rectangle, first calculate the width using the area formula: Area = length × width. Here, width = Area / length = 72 cm² / 9 cm = 8 cm. The perimeter is then calculated using the formula: Perimeter = 2(length + width) = 2(9 cm + 8 cm) = 34 cm.