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JhaicanBabila
@JhaicanBabila
May 2023
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Find the Surface Area/SA with solution
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jasminoratedizon
Verified answer
To find the surface area of a square pyramid with side length 5 cm and height 7 cm, we need to find the area of each face and add them together.
The base of the pyramid is a square with side length 5 cm, so its area is 5 cm x 5 cm = 25 cm^2.
To find the area of each triangular face, we need to find the length of the slant height. The slant height can be found using the Pythagorean theorem:
slant height = sqrt((side/2)^2 + height^2) = sqrt((5/2)^2 + 7^2) = sqrt(25/4 + 49) = sqrt(173)/2 ≈ 6.59 cm
Each triangular face has a base of length 5 cm and a height of 6.59 cm, so its area is:
(1/2) x base x height = (1/2) x 5 cm x 6.59 cm ≈ 16.48 cm^2
Therefore, the total surface area of the square pyramid is:
25 cm^2 + 4 x 16.48 cm^2 = 25 cm^2 + 65.92 cm^2 = 90.92 cm^2
To find the surface area of a sphere with radius 3.8 cm, we use the formula:
surface area = 4πr^2
where π is pi (approximately 3.14159) and r is the radius. Substituting the given value, we get:
surface area = 4 x 3.14159 x (3.8 cm)^2 ≈ 180.955 cm^2
Therefore, the surface area of the sphere is approximately 180.955 cm^2.
To find the surface area of a cylinder with radius 4 cm and height 3 cm, we use the formula:
surface area = 2πr^2 + 2πrh
where r is the radius and h is the height. Substituting the given values, we get:
surface area = 2 x 3.14159 x (4 cm)^2 + 2 x 3.14159 x 4 cm x 3 cm ≈ 150.796 cm^2
Therefore, the surface area of the cylinder is approximately 150.796 cm^2.
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Answers & Comments
Verified answer
To find the surface area of a square pyramid with side length 5 cm and height 7 cm, we need to find the area of each face and add them together.The base of the pyramid is a square with side length 5 cm, so its area is 5 cm x 5 cm = 25 cm^2.
To find the area of each triangular face, we need to find the length of the slant height. The slant height can be found using the Pythagorean theorem:
slant height = sqrt((side/2)^2 + height^2) = sqrt((5/2)^2 + 7^2) = sqrt(25/4 + 49) = sqrt(173)/2 ≈ 6.59 cm
Each triangular face has a base of length 5 cm and a height of 6.59 cm, so its area is:
(1/2) x base x height = (1/2) x 5 cm x 6.59 cm ≈ 16.48 cm^2
Therefore, the total surface area of the square pyramid is:
25 cm^2 + 4 x 16.48 cm^2 = 25 cm^2 + 65.92 cm^2 = 90.92 cm^2
To find the surface area of a sphere with radius 3.8 cm, we use the formula:
surface area = 4πr^2
where π is pi (approximately 3.14159) and r is the radius. Substituting the given value, we get:
surface area = 4 x 3.14159 x (3.8 cm)^2 ≈ 180.955 cm^2
Therefore, the surface area of the sphere is approximately 180.955 cm^2.
To find the surface area of a cylinder with radius 4 cm and height 3 cm, we use the formula:
surface area = 2πr^2 + 2πrh
where r is the radius and h is the height. Substituting the given values, we get:
surface area = 2 x 3.14159 x (4 cm)^2 + 2 x 3.14159 x 4 cm x 3 cm ≈ 150.796 cm^2
Therefore, the surface area of the cylinder is approximately 150.796 cm^2.