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Surface Area of A Hemisphere: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Surface Area of A HemisphereSurface Area of A Hemisphere: Definition and ExamplesTable of ContentsSurface Area of a Hemisphere Definition of Surface Area of a Hemisphere

The surface area of a hemisphere is the total area covered by the outer surface of a hemisphere, measured in square units. A hemisphere has two surfaces: a curved surface and a flat circular base. The curved surface area of a hemisphere is half the surface area of a sphere, which can be calculated using the formula 2πr22\pi r^22πr2, where 'rrr' is the radius of the hemisphere.

A hemisphere is a three-dimensional shape that is half of a sphere, created when a sphere is cut into two equal halves by a plane. The total surface area of a hemisphere combines both the curved surface area and the base area, resulting in the formula 3πr23\pi r^23πr2. For hollow hemispheres, which have both inner and outer curved surfaces plus a ring-shaped base, the formula becomes 3πR2+πr23\pi R^2 + \pi r^23πR2+πr2, where 'RRR' is the outer radius and 'rrr' is the inner radius.

Examples of Surface Area of a Hemisphere Example 1: Finding the Surface Area of a Hemisphere with Given Radius Problem:

Find the surface area of the hemisphere if its radius is 141414 units?

Step-by-step solution:

Step 1, Write down what we know. The radius of the hemisphere is 141414 units.

Step 2, Remember the formula for total surface area of a hemisphere: TSA=3πr2TSA = 3\pi r^2TSA=3πr2

Step 3, Put the value of radius into our formula: TSA=3×227×14×14TSA = 3\times \frac{22}{7} \times 14 \times 14TSA=3×722​×14×14

Step 4, Simplify the math step-by-step: TSA=3×22×2×14=1,848TSA = 3 \times 22 \times 2 \times 14 = 1,848TSA=3×22×2×14=1,848 square units

Step 5, Write the final answer. The total surface area of the hemisphere is 1,8481,8481,848 square units.

Example 2: Finding the Surface Area of a Hollow Hemisphere Problem:

Find the surface area of a hollow hemisphere whose outer radius measures 202020 units and inner radius is 101010 units. (Use π=3.14π = 3.14π=3.14)

Step-by-step solution:

Step 1, List the given values. The outer radius (RRR) of the hemisphere = 202020 units and the inner radius (rrr) = 101010 units.

Step 2, Recall the formula for the total surface area of a hollow hemisphere: TSA=3πR2+πr2TSA = 3\pi R^2 + \pi r^2TSA=3πR2+πr2

Step 3, Put the values into the formula: TSA=[3π×(20)2]+[π×(10)2]TSA = [3\pi \times (20)^2] + [\pi \times (10)^2]TSA=[3π×(20)2]+[π×(10)2]

Step 4, Calculate each part separately: TSA=(3×3.14×400)+(3.14×100)TSA = (3 \times 3.14 \times 400) + (3.14 \times 100)TSA=(3×3.14×400)+(3.14×100)

Step 5, Complete the calculation: TSA=3,768+314=4,082TSA = 3,768 + 314 = 4,082TSA=3,768+314=4,082 square units

Step 6, State the answer. The surface area of the hollow hemisphere is 4,0824,0824,082 square units.

Example 3: Finding the Radius from the Curved Surface Area Problem:

Calculate the radius of a hemisphere if its curved surface area is 500500500 sq. in.

Step-by-step solution:

Step 1, Write what we know. The curved surface area (AAA) is 500500500 square inches.

Step 2, Remember the formula for curved surface area of a hemisphere: A=2πr2A = 2\pi r^2A=2πr2

Step 3, Set up an equation to solve for rrr:

A=2πr2A = 2\pi r^2A=2πr2 500=2πr2500 = 2\pi r^2500=2πr2

Step 4, Rearrange to solve for r2r^2r2:

r2=A2πr^2 = \frac{A}{2\pi}r2=2πA​ r2=5002×3.14r^2 = \frac{500}{2 \times 3.14}r2=2×3.14500​

Step 5, Calculate the value of r2r^2r2: r2=2503.14=79.617r^2 = \frac{250}{3.14} = 79.617r2=3.14250​=79.617

Step 6, Find the radius by taking the square root: r=79.617=8.922r = \sqrt{79.617} = 8.922r=79.617​=8.922 inches

Step 7, State the final answer. The radius of the hemisphere is 8.9228.9228.922 inches.

Comments(2)GGraphicDesignerSamNovember 4, 2025I've been struggling to explain hemisphere surface area to my students. This page's clear def and examples made it a breeze! Thanks!

NNatureLover89September 17, 2025This page was a lifesaver! I used the step-by-step examples to help my kids understand hemispheres better. The clear explanations made it so easy to teach them about surface area!

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