The image above is a spherical cap. To calculate the curved surface area of a spherical cap requires two essential parameters which are the radius of the base of the cap (a) and the height (h).

The formula for calculating the curved surface area of the spherical cap:

A = Ï€(aÂ² + hÂ²)

Where;

A = Curved surface area of the spherical cap

a = Radius of the base of the cap

h = Height of the spherical cap

Let’s solve an example;

Find the curved surface area of a spherical cap with radius of the base 7 cm and the height of 13 cm.

This implies that;

a = Radius of the base of the cap = 7 cm

h = Height of the spherical cap = 13 cm

A = Ï€(aÂ² + hÂ²)

A =Â Ï€(7Â² + 13Â²)

Then, A =Â Ï€(49 + 169)

A =Â Ï€(218)

A = 684.867

Therefore, the **curved surface area of the spherical cap** is **684.867 cmÂ².**

**Calculating the Radius of the base of a Spherical Cap using the Curved Surface Area of the Spherical Cap and the Height**

a = âˆš^{A – Ï€h2} / _{Ï€}

Where;

A = Curved surface area of the spherical cap

a = Radius of the base of the cap

h = Height of the spherical cap

Let’s solve an example;

Find the radius of the base of a spherical cap when the curved surface area of the spherical cap is 300 cm^{2} and a height of 7 cm.

This implies that;

A = Curved surface area of the spherical cap = 300Â cm^{2}

h = Height of the spherical cap = 7 cm

a = âˆš^{A – Ï€h2} / _{Ï€}

a = âˆš^{300 – 3.142 x 72} / _{Ï€}

So, a = âˆš^{300 – 3.142 x 49} / _{Ï€}

a = âˆš^{300 – 153.958} / _{Ï€}

a = âˆš^{146.042} / _{Ï€}

That is, a = âˆš46.48

a = 6.82

Therefore, the **radius of the base of the cap** is **6.82 cm.**

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**Calculating the Height of a Spherical Cap using the Curved Surface Area of the Spherical Cap and the Radius of the base of the Cap**

h = âˆš^{A – Ï€a2} / _{Ï€}

Where;

A = Curved surface area of the spherical cap

a = Radius of the base of the cap

h = Height of the spherical cap

Let’s solve an example;

Find the height of a spherical cap when the curved surface area of the spherical cap is 420 cm^{2} and the radius of the base of the cap is 9 cm.

This implies that;

A = Curved surface area of the spherical cap = 420Â cm^{2}

r = Radius of the base of the spherical cap = 9 cm

h = âˆš^{A – Ï€a2} / _{Ï€}

h = âˆš^{420 – 3.142 x 92} / _{Ï€}

That is, h = âˆš^{420 – 3.142 x 81} / _{Ï€}

h = âˆš^{420 – 254.502} / _{Ï€}

h = âˆš^{165.498} / _{Ï€}

Then, h = âˆš52.67

h = 7.26

Therefore, the** height of the spherical cap** is **7.26 cm.**

Read more:Â How to Calculate and Solve for the Volume of a Spherical Cap | Nickzom Calculator

**How to Calculate the Curved Surface Area of a Spherical Cap Using Nickzom Calculator**

Nickzom Calculator â€“Â **The Calculator Encyclopedia**Â is capable of calculating the curved surface area of the spherical cap.

To get the answer and workings of the curved surface area of the spherical cap using theÂ **Nickzom Calculator â€“ The Calculator Encyclopedia.Â **First, you need to obtain the app.

You can get this app via any of these means:

**Web**Â â€“Â https://www.nickzom.org/calculator-plus

To get access to theÂ **professionalÂ **version via web, you need toÂ **register**Â andÂ **subscribeÂ **for**Â NGN 1,500Â **per**Â annum**Â to have utter access to all functionalities.

You can also try theÂ **demoÂ **version viaÂ https://www.nickzom.org/calculator

**Android (Paid)**Â â€“Â https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)**Â â€“Â https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)**Â â€“Â https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to theÂ **Calculator Map,Â **then click onÂ **Mensuration****Â **under theÂ **Mathematics**Â section.

Now, click on **Curved Surface AreaÂ of the spherical cap**Â underÂ **Mensuration**

The screenshot below displays the page or activity to enter your values, to get the answer for the curved surface area of the spherical cap according to the respective parameters which are the radius of the base of the cap (a) and height (h).

Now, enter the values appropriately and accordingly for the parameters as required by theÂ **example**Â above where the**Â radius of the base of the capÂ **is **7 cmÂ **and**Â the heightÂ **is **13Â cm.**

Finally, Click on Calculate

As you can see from the screenshot above,Â **Nickzom Calculator**Â â€“ The Calculator Encyclopedia solves for the**Â Curved Surface Area of a spherical cap**Â and presents the formula, workings and steps too.