Capsule Surface Area Calculator

BySteven

Enter the values of base radius, height to calculate top & bottom surface area, Lateral and total surface area. For more understanding read the solved examples and formulas below.

Capsule Surface Area Calculator

The Capsule Surface Area Calculator is a powerful online calculator to help Professionals to helps them accurately design and construct capsule shapes objects. Here we have explored more with formulas and examples.

Formula:

The formula is:

A=4πr2+2πrhA = 4\pi r^2 + 2\pi rh

Variables

VariableMeaning
ASurface Area of the capsule
rrRadius of the spherical ends of the capsule
hhHeight (or length) of the cylindrical part of the capsule

Solved Examples:

Example 1:

Given:

  • Radius () = 3 cm
  • Height () = 10 cm
CalculationInstructions
Step 1: A=4πr2+2πrhA = 4\pi r^2 + 2\pi rhStart with the formula.
Step 2: A=4π(3)2+2π(3)(10)A = 4\pi (3)^2 + 2\pi (3)(10)Replace r with 3 cm and h with 10 cm.
Step 3: A=4π(9)+2π(30)A = 4\pi (9) + 2\pi (30)Calculate r2=9r^2 = 9 and multiply r×h=30r \times h = 30
Step 4: A=36π+60πA = 36\pi + 60\piMultiply 4×9=364 \times 9 = 36 and 2×30=602 \times 30 = 60
Step 5: A=96πA = 96\piAdd the two terms.
Step 6: A≈301.59 cm2A \approx 301.59 \, \text{cm}^2Multiply by π≈3.14159\pi \approx 3.14159 to get the surface area.

Answer: The surface area of the capsule is approximately 301.59 cm².

Capsule Surface Area Calculator

Example 2:

Given:

  • Radius (r) = 5 cm
  • Height (h) = 8 cm
CalculationInstructions
Step 1: A=4πr2+2πrhA = 4\pi r^2 + 2\pi rhStart with the formula.
Step 2: A=4π(5)2+2π(5)(8)A = 4\pi (5)^2 + 2\pi (5)(8)Replace r with 5 cm and with 8 cm.
Step 3: A=4π(25)+2π(40)A = 4\pi (25) + 2\pi (40)Calculate r2=25r^2 = 25 and multiply r×h=40r \times h = 40
Step 4: A=100π+80πA = 100\pi + 80\piMultiply 4×25=1004 \times 25 = 100 and 2×40=802 \times 40 = 80
Step 5: A=180πA = 180\piAdd the two terms.
Step 6: A≈565.49 cm2A \approx 565.49 \, \text{cm}^2Multiply by π≈3.14159\pi \approx 3.14159 to get the surface area.

Answer: The surface area of the capsule is approximately 565.49 cm².

What is Capsule Surface Area Calculator ?

The Capsule Surface Area Calculator used to calculate the total surface area of a capsule-shaped object. A capsule is a geometric shape that consists of a cylinder with hemispherical ends on both sides. The surface area of the capsule is made up of the surface area of the cylindrical part and the surface areas of the two hemispherical ends.

The formula A=4πr2+2πrhA = 4\pi r^2 + 2\pi rh calculates this total surface area by adding the surface area of the two hemispheres (which together form a full sphere) and the surface area of the cylindrical part.

Final Words:

Capsule Surface area calculation are essential in certain fields like pharmacology, engineering etc in shapes design. For accurate calculation use the calculator above and for better understanding see the solved examples.

 

Steven

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