Question
Find the Total surface area of the hemisphere (in $cm^2$) whose radius is $48cm$ and $\pi = 3.14$.
The correct answer is
21703.68
Hemisphere Surface Area Calculation
To find the total surface area of a hemisphere, we use the formula:
$ \text{Total Surface Area} = 2\pi r^2 + \pi r^2 = 3\pi r^2 $
Where:
- $r$ is the radius of the hemisphere
- $\pi$ is the mathematical constant Pi
Given Values:
- Radius ($r$) = $48$ cm
- Pi ($\pi$) = $3.14$
Calculation Steps:
- Substitute the given values into the total surface area formula:
$ \text{Total Surface Area} = 3 \times 3.14 \times (48 \text{ cm})^2 $
- Calculate the square of the radius:
$ (48 \text{ cm})^2 = 2304 \text{ cm}^2 $
- Multiply the numerical values:
$ \text{Total Surface Area} = 3 \times 3.14 \times 2304 \text{ cm}^2 $
$ \text{Total Surface Area} = 9.42 \times 2304 \text{ cm}^2 $
- Perform the final multiplication to get the result:
$ \text{Total Surface Area} = 21703.68 \text{ cm}^2 $
The total surface area of the hemisphere is $21703.68$ cm$^2$.
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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:
- 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.)
- Find the Total surface area of the hemisphere (in $cm^2$) whose radius is 26cm and $\pi = 3.14$.
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