Cube Volume to Side Length
The volume of a cube is given by the formula $V = s^3$, where $s$ is the side length.
We are given the volume $V = 1728\text{ cm}^3$. To find the side length $s$, we take the cube root:
$s = \sqrt[3]{1728\text{ cm}^3}$
Since $12 \times 12 \times 12 = 1728$, the side length of the cube is:
$s = 12\text{ cm}$
Sphere Dimensions from Cube
A sphere inscribed inside a cube has a diameter equal to the side length of the cube.
- Cube side length, $s = 12\text{ cm}$
- Sphere diameter, $d = s = 12\text{ cm}$
- Sphere radius, $r = \frac{d}{2} = \frac{12\text{ cm}}{2} = 6\text{ cm}$
Sphere Surface Area Calculation
The formula for the total surface area ($SA$) of a sphere is $SA = 4\pi r^2$.
Using the calculated radius $r = 6\text{ cm}$:
$SA = 4\pi (6\text{ cm})^2$
$SA = 4\pi (36\text{ cm}^2)$
$SA = 144\pi\text{ cm}^2$
Therefore, the total surface area of the sphere is $144\pi\text{ cm}^2$. This matches Option A.
Similar Questions
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Important Questions from Mensuration
The areas of three adjacent faces of a cuboidal tank are 3 m 2, 12 m 2 and 16 m 2. the capacity of the tank, in litres, is:
Volume of a cuboid is 4800 cm 3. If the height of this cuboid is 20 cm, then what will be the area of the base of cuboid ?
Two similar cubes have heights of 8 cm and 12 cm, respectively. If the capacity of the smaller cube is 80 cm 3, what is the capacity of the bigger cube (in cm 3)?
Three circles of radius 7 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
Three circles of radius 6 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
