Hemisphere Surface Area Calculation
To calculate the total surface area (TSA) of a hemisphere, we first need to determine its radius from the given diameter.
Given Hemisphere Details
- Diameter of the hemisphere, $d = 7$ cm.
- The radius ($r$) is half the diameter: $r = \frac{d}{2} = \frac{7 \text{ cm}}{2} = 3.5 \text{ cm}$.
Surface Area Formula Recall
The formula for the total surface area (TSA) of a hemisphere is:
TSA $= 2 \pi r^2 + \pi r^2 = 3 \pi r^2$
Here, $r$ is the radius and we use the approximation $\pi \approx \frac{22}{7}$.
Step-by-Step Calculation
- Substitute the radius ($r = 3.5$ cm) into the TSA formula:
TSA $= 3 \times \frac{22}{7} \times (3.5 \text{ cm})^2$
- Calculate the square of the radius:
$(3.5 \text{ cm})^2 = 3.5 \times 3.5 \text{ cm}^2 = 12.25 \text{ cm}^2$
- Multiply the terms:
TSA $= 3 \times \frac{22}{7} \times 12.25 \text{ cm}^2$
TSA $= 3 \times 22 \times \frac{12.25}{7} \text{ cm}^2$
TSA $= 3 \times 22 \times 1.75 \text{ cm}^2$
TSA $= 66 \times 1.75 \text{ cm}^2$
- Compute the final value:
TSA $= 115.5 \text{ cm}^2$
The total surface area of the hemisphere is $115.5 \text{ cm}^2$.
Similar Questions
- The radius of a sphere is 16 cm. Find its surface area.
- What is the ratio of volumes of two spheres where the curved surface areas are in the ratio of $1 : 4$?
- Five solid cubes, each of volume $39304 \text{ cm}^3$, are joined end to end to form a cuboid. What is the lateral surface area (in $\text{cm}^2$) of the cuboid?
- What is the surface area of a sphere of radius 8 cm? (use $\pi = 3.14$)
- The ratio of the volumes of two cubes is 64 : 1331. What is the ratio of their total surface areas?
- The diameters of the bases of two cones are equal. If their slant heights are in the ratio of 3 : 4, then what will the ratio of their curved surface areas be?
- A cube of volume 324 cm$^3$ is molded into a cuboid whose length, width and height are in the ratio $3 : 2 : 2$. Find the length of the cuboid.
- An aquarium is in the form of a cuboid whose external measures are $80 \text{ cm} \times 30 \text{ cm} \times 40 \text{ cm}$. The base, side faces and back face are to be covered with a coloured paper. Find the area of the paper needed?
- A godown is in the form of a cuboid of measures $60 \text{ m} \times 40 \text{ m} \times 30 \text{ m}$. How many cuboidal boxes can be stored in it if the volume of one box is $0.8 \text{ m}^3$?
- Find the number of bricks measuring 25 cm in length, 5 cm in breadth and 20 cm in height for a wall 40 m long, 80 cm broad and 6 m in height.
Important Questions from 3-D Mensuration
Find the total surface area of a closed cylinder having a base radius of 70 m and a height of 110 m. [Use π = \(22\over7\)]
- The curved surface area of a cylinder is half of its total surface area. If its height is 195 cm, then find its diameter (in cm).
The diameter of the base and slant height of a right circular cone are 30 cm and 113 cm, respectively. Find the volume (in cm³) of the given cone.
(Use $\pi = \frac{22}{7}$)- A cylindrical rod has an curved surface area of $4,900 \text{ cm}^2$. If the length of the rod is 97 cm, then the radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$ - The volume (in $m^3$) of a cube, each of whose edges is 42 m, is:
