Calculating Sphere Surface Area
To find the surface area of a sphere, we use a specific formula that relates the area to the sphere's radius.
Given Information
The radius ($r$) of the sphere is given as 16 cm.
Surface Area Formula
The formula for the surface area ($A$) of a sphere is:
$ A = 4\pi r^2 $
Calculation Steps
-
Substitute the given radius ($r = 16$ cm) into the formula:
$ A = 4\pi (16 \text{ cm})^2 $
-
Calculate the square of the radius:
$ (16 \text{ cm})^2 = 256 \text{ cm}^2 $
-
Multiply the result by $4\pi$:
$ A = 4\pi \times 256 \text{ cm}^2 $
$ A = 1024\pi \text{ cm}^2 $
Final Answer
The surface area of the sphere is $1024\pi \text{ cm}^2$. This corresponds to Option 4.
Similar Questions
- 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 diameter of a hemisphere is 7 cm. What will its total surface area be?
- 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:
