Surface Area Worksheet 1

Are you a math teacher or a student who needs practice with calculating surface area? Look no further! Welcome to Surface Area Worksheet 1, where you will find a variety of exercises to help you strengthen your understanding of this important concept. Whether you're in middle school, high school, or just need some extra practice, this worksheet is the perfect resource for you.

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What is the formula for finding the surface area of a rectangular prism?

The formula for finding the surface area of a rectangular prism is given by 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the rectangular prism.

Determine the surface area of a cube with side length 5 cm.

The surface area of a cube can be calculated by finding the sum of the areas of all six faces. Since all faces of a cube are identical squares, the surface area of a cube with side length 5 cm is 6 times the area of one face, which is 6 x (5 cm x 5 cm) = 150 square cm.

Calculate the surface area of a cylinder with radius 3 cm and height 10 cm.

The formula for calculating the surface area of a cylinder is 2?r(r + h), where r is the radius and h is the height. Substituting the given values, the surface area of the cylinder is 2?(3 cm)(3 cm + 10 cm) = 2?(3 cm)(13 cm) = 78? cm^2, which is approximately 245.04 cm^2.

Find the surface area of a triangular prism with base dimensions 6 cm, 8 cm, and 10 cm, and height 12 cm.

To find the surface area of a triangular prism, we need to calculate the areas of the two triangular bases and the three rectangular faces. The area of each triangular base is 1/2*base*height, so each base has an area of 1/2*6*12 = 36 cm^2. The three rectangular faces each have an area equal to the base times the height, so the total surface area is 2*(36 cm^2) + 3*(6 cm * 12 cm) = 72 cm^2 + 216 cm^2 = 288 cm^2. Thus, the surface area of the triangular prism is 288 cm^2.

A sphere has a radius of 4 cm. What is its surface area?

The surface area of a sphere is given by the formula 4?r^2, where r is the radius of the sphere. Plugging in the radius of 4 cm, the surface area of the sphere would be 4?(4)^2 = 4?(16) = 64? cm². Thus, the surface area of the sphere with a radius of 4 cm is 64? square centimeters.

Determine the surface area of a pyramid with a square base measuring 6 cm on each side and a slant height of 9 cm.

To find the surface area of a pyramid, first calculate the area of the base by squaring the length of one side (6 cm x 6 cm = 36 cm^2). Next, calculate the area of each triangular face by multiplying the base (6 cm) by half the slant height (9 cm) and dividing by 2 (6 cm x 9 cm / 2 = 27 cm^2). Since there are 4 triangular faces on a pyramid, multiply the area of one triangular face by 4 (27 cm^2 x 4 = 108 cm^2). Add the base area (36 cm^2) to the total area of the triangular faces to get the surface area of the pyramid, which is 144 cm^2.

Find the total surface area of a cone with radius 2 cm and slant height 6 cm.

The total surface area of a cone is calculated by adding the curved surface area and the base area. The curved surface area is given by ?rs, where r is the radius and s is the slant height. Substituting the values, we get ?(2)(6) = 12? cm². The base area of a cone is ?r², so substituting the values, we get ?(2)² = 4? cm². Therefore, the total surface area of the cone is 12? + 4? = 16? cm², which is approximately 50.27 cm².

Calculate the surface area of a rectangular prism with length 7 cm, width 5 cm, and height 3 cm.

The surface area of a rectangular prism can be calculated by adding the areas of all six faces. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Plugging in the values provided: 2(7)(5) + 2(7)(3) + 2(5)(3) = 70 + 42 + 30 = 142 cm². Therefore, the surface area of the rectangular prism is 142 square centimeters.

The surface area of a triangular prism is 120 cm². If the base has dimensions 6 cm by 8 cm, what is its height?

To find the height of the triangular prism, we first need to calculate the lateral surface area of the prism. The lateral surface area formula for a triangular prism is L = perimeter of base * height. Given that the base has dimensions 6 cm by 8 cm, the perimeter of the base is 2 * (6 + 8) = 28 cm. If the total surface area is 120 cm², we subtract the area of the two triangular bases (2 * 6 * 8 = 96 cm²) from the total surface area to get the lateral surface area: 120 cm² - 96 cm² = 24 cm². Substitute the lateral surface area and the perimeter of the base into the formula: 24 cm² = 28 cm * height. Solving for height, we get height = 24 cm² / 28 cm = 0.857 cm. Therefore, the height of the triangular prism is 0.857 cm.

Find the surface area of a hemisphere with a diameter of 10 cm.

To find the surface area of a hemisphere with a diameter of 10 cm, we first need to calculate the radius, which is half the diameter, so 10/2 = 5 cm. The formula for the surface area of a hemisphere is SA = 2?r^2, where r is the radius. Plugging in the values, we get SA = 2 * ? * (5)^2 = 2 * ? * 25 = 50? cm^2. Therefore, the surface area of the hemisphere is 50? square centimeters.