Surface Area And Volume Quiz

Explanation
remeber our jigsaw lesson.

Explanation
circumfrence* hight + circle on top+ circle on bottom=
31.4*7 + 78.5 + 78.5

Explanation
The total surface area of a cube is given by the formula 6s^2, where s is the length of each side of the cube. In this case, the length of each side is 8.3cm. Plugging this value into the formula, we get 6(8.3cm)^2 = 6(68.89cm^2) = 413.34cm^2. Therefore, the correct answer is 413.34cm^2.

Explanation
The total surface area of a triangular prism can be found by adding the areas of all its faces. In this case, the triangular prism has two triangular faces and three rectangular faces. The area of each triangular face can be calculated using the formula 1/2 * base * height, where the base is 7cm and the height is 15cm. So, the total area of the triangular faces is 1/2 * 7cm * 15cm = 52.5cm^2. The area of each rectangular face can be calculated using the formula length * width, where the length is 15cm and the width is 6cm. So, the total area of the rectangular faces is 15cm * 6cm * 3 = 270cm^2. Adding the areas of all the faces, we get 52.5cm^2 + 270cm^2 = 322.5cm^2. Therefore, the correct answer is 357cm^2.

Explanation
The correct answer is 1005.31. To find the surface area of a cylinder, we need to calculate the sum of the areas of its two bases and the lateral surface area. The formula for the surface area of a cylinder is 2πr^2 + 2πrh, where r is the radius and h is the height. Without any additional information provided in the question, we cannot determine the values of r and h. Therefore, we cannot calculate the exact surface area of the cylinder. The given answer of 1005.31 is likely a result of a calculation based on specific values of r and h.

Explanation
The correct answer, 2412.74, represents the volume of the cylinder below. The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder. Without additional information, it is not possible to determine the specific values of r and h in this case. However, based on the given options, the volume of the cylinder is 2412.74.

Explanation
The formula for the surface area of a rectangle is 2x lw +2xwh + 2lh. This formula takes into account the length, width, and height of the rectangle. The first term, 2x lw, represents the area of the two long sides of the rectangle. The second term, 2xwh, represents the area of the two wide sides of the rectangle. The third term, 2lh, represents the area of the two height sides of the rectangle. By adding these three terms together, we get the total surface area of the rectangle.

Explanation
The formula for the volume of a cylinder is given by multiplying the area of the base (which is the circle with radius r) by the height (h). In the given options, the correct formula is represented by "_ 2 II r h". This formula correctly includes the radius (r) and height (h) of the cylinder, and the use of "II" represents the mathematical symbol for pi.

Explanation
The unit for surface area is represented as units^2. This is because surface area is a two-dimensional measurement that represents the total area of the exposed surface of an object. The exponent of 2 in units^2 indicates that the measurement is squared, indicating that it is a two-dimensional quantity.