Last updated on August 5th, 2025
A prism or a cylinder is a 3-dimensional shape with flat faces or curved surfaces. The surface area of these shapes is the total area covered by their outer surfaces. The surface area for prisms includes the areas of all its faces, while for cylinders, it includes both the curved surface and the circular bases. In this article, we will learn about the surface area of prisms and cylinders.
The surface area of prisms and cylinders is the total area occupied by the boundaries or surfaces of these shapes. It is measured in square units.
A prism is a 3D shape with two identical bases and flat sides, while a cylinder has a curved surface and two circular bases. Prisms can be classified into different types based on the shape of their base, such as rectangular prisms and triangular prisms. Cylinders are generally circular.
For prisms, surface area includes the areas of all its faces, while for cylinders, it includes the curved surface area and the total surface area.
Prisms and cylinders have different surface area calculations based on their shapes: 1. Surface Area of Prisms 2. Surface Area of Cylinders
The surface area of a prism is the sum of the areas of all its faces. For a rectangular prism, the surface area is calculated as:
Surface Area = 2lw + 2lh + 2wh square units
Where l is the length, w is the width, and h is the height of the prism.
The total area occupied by the cylinder, including the area of the curved surface and the area of the two circular bases, is known as the total surface area of a cylinder. The total surface area is calculated using the formula:
Total Surface Area = 2πr(h + r) square units
Where r is the radius of the base of the cylinder and h is the height of the cylinder.
The volume of a cylinder shows how much space is inside it. It tells us how much it can hold.
The volume of a cylinder can be found by using the formula: Volume = πr²h cubic units
Students sometimes confuse the formulas and calculations for surface area and volume. Remember that surface area measures the outer surface, while volume measures the space inside.
Given l = 8 cm, w = 5 cm, h = 10 cm. Use the formula: Surface Area = 2lw + 2lh + 2wh = 2(8)(5) + 2(8)(10) + 2(5)(10) = 80 + 160 + 100 = 340 cm²
Find the total surface area of a cylinder with a radius of 4 cm and a height of 9 cm.
Total Surface Area = 326.56 cm²
Use the formula: Total Surface Area = 2πr(h + r) = 2 × 3.14 × 4 × (9 + 4) = 2 × 3.14 × 4 × 13 = 326.56 cm²
A cylinder has a radius of 5 cm and a height of 12 cm. Find the total surface area.
Total Surface Area = 534.6 cm²
Use the formula: Total Surface Area = 2πr(h + r) = 2 × 3.14 × 5 × (12 + 5) = 2 × 3.14 × 5 × 17 = 534.6 cm²
Find the surface area of a triangular prism with a base perimeter of 24 cm, a base area of 30 cm², and a height of 10 cm.
Surface Area = 480 cm²
Surface Area = (Base Perimeter × Height) + 2 × Base Area = (24 × 10) + 2 × 30 = 240 + 60 = 480 cm²
The radius of a cylinder is 7 cm, and its total surface area is 660 cm². Find the height.
Height = 10 cm
Students often make mistakes while calculating the surface area of prisms and cylinders, leading to incorrect answers. Below are some common mistakes and ways to avoid them.
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