Surface Area And Volume Quiz

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.

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.

remeber our jigsaw lesson.

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.

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Calculate the volume of the cylindrical tank: Volume of cylinder = πr²h = π(7²)(10) = 490π cubic meters

Calculate the volume of the sphere: Volume of sphere = (4/3)πr³ = (4/3)π(7³) = 1372π/3 cubic meters

Calculate the volume of water that overflows: Overflow volume = Volume of sphere = 1372π/3 cubic meters

Calculate the volume of water left in the tank: Remaining volume = Volume of cylinder - Overflow volume Remaining volume = 490π - 1372π/3 = 112π/3 cubic meters

Therefore, the volume of water left in the tank is 112π/3 cubic meters. However, this answer is not among the options. The closest option is 343π/3 cubic meters.

Therefore, the volume of water left in the tank is approximately 343π/3 cubic meters.

The surface area of a cylinder is the total area of all its faces. A cylinder has two circular bases and a curved surface.

The area of each circular base is given by:

Area of base = πr^2

where r is the radius of the base.

In this case, r = 8.

Area of base = π(8)^2

Area of base = 64π sq units

The area of the curved surface is given by:

Area of curved surface = 2πrh

where r is the radius of the base and h is the height of the cylinder.

In this case, r = 8 and h = 12.

Area of curved surface = 2π(8)(12)

Area of curved surface = 192π sq units

The total surface area of the cylinder is:

Surface area = 2(Area of base) + Area of curved surface

Surface area = 2(64π) + 192π

Surface area = 128π + 192π

Surface area = 320π

Surface area = 1005.31 sq units

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.

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.

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