Hemisphere Surface Area Calculation
This solution explains how to find the total surface area of a hemisphere given its radius and the value of pi ($\pi$).
Formula for Hemisphere Surface Area
The total surface area (TSA) of a hemisphere is the sum of its curved surface area and the area of its circular base.
- Curved Surface Area = $2\pi r^2$
- Base Area = $\pi r^2$
- Total Surface Area (TSA) = Curved Surface Area + Base Area = $2\pi r^2 + \pi r^2 = 3\pi r^2$
Where '$r$' is the radius of the hemisphere.
Step-by-Step Calculation
We are given:
- Radius ($r$) = $26$ cm
- Value of $\pi$ = $3.14$
Step 1: Substitute the values into the formula.
TSA = $3 \times \pi \times r^2$
TSA = $3 \times 3.14 \times (26)^2$ $cm^2$
Step 2: Calculate the square of the radius.
$r^2 = (26)^2 = 26 \times 26 = 676$ $cm^2$
Step 3: Multiply the values to find the total surface area.
TSA = $3 \times 3.14 \times 676$ $cm^2$
TSA = $9.42 \times 676$ $cm^2$
TSA = $6367.92$ $cm^2$
Therefore, the total surface area of the hemisphere is $6367.92$ $cm^2$.
Important Questions from Mensuration 3D (Notes)
- The height of a cylinder is 14cm and its curved surface area is 264cm². The volume of the cyclinder (in cm³) is:
($\pi=\frac{22}{7}$) - A cylindrical rod has an outer curved surface area of \(7500 \text{ cm}^2\). If the length of the rod is 92 cm, then the outer radius (in cm) of the rod, rounded off to two places of decimal, is:
\(\left(\text{Take } \pi = \frac{22}{7}\right)\) - A number of 512 identical small spheres are cast from a sphere of radius 40 cm, with the total volume of the small spheres being equal to the volume of the larger sphere. The diameter (in cm) of each of the small spheres is:
There is a wooden block in the form of a cube whose each side is 8 meters long.
The maximum possible number of cylinders with a diameter of 1 meter and a height of 4 meters were cut from this block. The cylinders are to be painted at the rate of ₹14 per square meter.
What is the total amount (in ₹) needed to paint all the cylinders if we paint the entire surface of each cylinder? (Take $\pi = \frac{22}{7}$)
- If the lateral surface area of a cylinder is 775.8 cm$^2$ and its height is 24 cm, then find its volume. (Use $\pi = 3.14$ and round off to two decimal places.)
