Surface Area Worksheets: Prisms, Pyramids, Spheres

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Surface Area Worksheets

Various surface area worksheets in finding the surface area of spheres and hemispheres, prisms such as cube, rectangular prisms, cylinders and pyramids with different bases such as square, rectangle, circle and triangle are included. One fine example for pyramid is cone.

Finding the surface area of the prisms are quite easier than other shapes. Find the perimeter of base of the prism and multiply it with height of the prism which provides lateral surface area of prism. Find the base areas separately and add them with lateral surface area.

In case of pyramids, we use a simple formula to find the total surface area.

Surface area of pyramids =1/2 * perimeter of the base * slant height of the pyramid + area of the base.

Combined surface area worksheets include word problems, simple problems, with decimals or without decimals and with or without approximation.


Rectangular Prism Worksheets:

Rectangular prisms are formed by six rectangular faces. As opposite faces are equal in area, we can arrive to simple formula, surface area = 2(lw + wh + hl), where l, w and h are length, width and height respectively.

Cube Worksheets:

Cube is kind of rectangular prim on which all edges are equal in length. As l = w = h in cubes, surface area of rectangular prism formula can be deduced to form a surface area of a cube. Each face equals a^2. Therefore, surface area = 6 * a^2

Cylinder Worksheets:

Cylinder is a prism with circle as a base. Circumference of a circle = 2 * pi * r and h is the height of the cylinder. Therefore, lateral surface area = 2 * pi * r * h. Area of circle = pi * r^2. As top and bottom are circles, total surface area of cylinder = 2*pi*r*h + 2*pi*r^2 = 2*pi*r*(r+h)

Cone Worksheets:

Cone is a pyramid with circle as a base. Perimeter of a circle = 2 * pi * r; Area of a circle = pi * r^2. Take l as slant height of the cone. Applying this in general formula for pyramids we have, surface area = 1/2 * (2*pi*r) * l + pi * r^2. Cancelling 2 and factoring out pi and r, we have S.A = pi * r * (l + r)

Sphere Worksheets:

Sphere is neither prism nor pyramid. Surface area of a sphere = 4 * pi * r^2. Worksheets with exact and approximate answers and word problems are included.

Hemisphere Worksheets:

Half of sphere is hemisphere. Lateral surface area = 2 * pi *r^2. Area of the base = pi * r^2. Therefore, total surface area of a hemisphere = 2 * pi * r^2 + pi * r^2 = 3*pi*r^2

Rectangular Pyramid Worksheets:

Perimeter of a rectangle = 2(l+w); s = side length or slant height of the face; Area of a rectangle = l * w; Apply these information in general formula to find the surface area of rectangular pyramids.

Square Pyramid Worksheets:

Perimeter of a square = 4a, where 'a' is the side of a square. Let s is the side length or slant height of square pyramid. Area of a square = a^2. Find the surface area of square pyramid by applying them.

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