To find the volume of the sphere formed by joining two hemispheres, we start by understanding the relationship between the curved surface area and volume of a sphere.
- Begin with the curved surface area of a hemisphere, which is given by \(2\pi r^2\). According to the question, each hemisphere has a curved surface area of \(8\pi \text{ cm}^2\).
- Using the formula for the hemisphere's curved surface area: \(2\pi r^2 = 8\pi\)
- Solving for \(r^2\), we get \(r^2 = 4\)
- Thus, the radius \(r = 2 \text{ cm}\)
- Now, calculate the volume of the sphere using the formula: \(V = \frac{4}{3}\pi r^3\).
- Substitute \(r = 2 \text{ cm}\) into the volume formula:
- \(V = \frac{4}{3}\pi (2)^3\)
- \(V = \frac{4}{3}\pi \times 8\)
- \(V = \frac{32\pi}{3} \text{ cm}^3\)
- Therefore, the volume of the sphere formed is \(\frac{32\pi}{3} \text{ cm}^3\), which corresponds to the option
\(32\pi/3\)
- .
The correct answer is \(\frac{32\pi}{3}\).
Similar Questions
Find the total surface area of a closed cylinder having a base radius of 70 m and a height of 110 m. [Use π = \(22\over7\)]
Which of the following is a geometrical figure with a three-dimensional geometry that has eight vertices and six rectangular faces?
- A solid metal sphere is melted and smaller spheres of equal radii are formed. 5% of the volume of the sphere is lost during the process. The smaller sphere has a radius that is one-tenth of the large sphere. If 14 liters of paint was needed to paint the larger sphere, how many liters is needed to paint all the smaller spheres?
A conical tent has a base radius of 14 m and a height of 48 m. How many cubic meters of air can it hold? (Use \(\pi\) = )
The circumference of the base of a solid right circular cylinder is 88 cm and its height is 150 cm. What is the volume (in cm3) of the cylinder?
A solid right circular cone is 7 cm high, and the radius of its base is 22.2 cm. It is melted and recast into a right circular cone with radius of its base 3.7 cm. Then the height (in cm) of the cone is ______.
A plane parallel to the base divides a cone of height 40 cm into two parts. If the volumeof the upper smaller cone formed is \(\frac{1}{64}\) of the volume of the original cone, calculate the height of the plane from the base of the cone.
In a workshop, you need to fill a cylindrical tank with a liquid. The tank has a diameter of 1 meter and a height of 2 meters. Which method will give you the most accurate measurement of the tank's volume before filling it?
If the volume of a cube is 3375 cm3, what is the length of one side?
The total surface area of a cylinder is given by ________.
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 = \(22\over7\)]
Which of the following is a geometrical figure with a three-dimensional geometry that has eight vertices and six rectangular faces?
- 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 $\pi = \frac{22}{7}$
