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Surface area of Sphere and Hemisphere - Surface Areas and Volumes, Class 9, Mathematics | Extra Documents & Tests for Class 9 PDF Download
SPHERE
Objects like football, volleyball, throw-ball etc. are said to have the shape of a sphere. In mathematical terms, a sphere is a solid generated by revolving a circle about any of its diameters. Let a thin circular disc of card board with centre O and radius r revolve about its diameter AOB to describe a sphere as shown in figure.
Here, O is called the centre of the sphere and r is radius of the sphere. Also, the line segment AB is a diameter of the sphere
For a solid sphere of radius = r, we have :
SPHERICAL SHELL
The solid enclosed between two concentric spheres is called a spherical shell.
For a spherical shell with external radius = R and internal radius = r, we have :
Question for Surface area of Sphere and Hemisphere - Surface Areas and Volumes, Class 9, MathematicsTry yourself: Which of the following statements about a sphere is true?View Solution
HEMISPHERE
When a plane through the centre of a sphere cuts it into two equal parts, then each part is called a hemisphere.
From a solid sphere, the obtained hemisphere is also a solid and it has a base as shown in fig.
For a hemisphere of radius r, we have :
HEMISPHERICAL SHELL
The solid enclosed between two concentric hemispheres is called a hemispherical shell.
For a hemispherical shell of external radius = R and internal radius = r, we have :
Ex.1 Find the surface area of a sphere of diameter 14cm.
Sol. Diameter = 14 cm
Ex.2 Find the radius of sphere whose surface area is 314 cm2. (Use π= 3.14)
Sol. Let r cm be the radius of the sphere whose surface area = 314 cm2
Ex.3 Find the total surface area of a hemisphere of radius 10 cm. (Use π= 3.14)
Sol. r = 10 cm.
∴ Total Surface area of the hemisphere = 3πr2 = 3 x 3.14 x (10)2 = 942 cm2
Ex.4 A hemispherical bowl is made from a metal sheet having thickness 0.3 cm. The inner radius ofthe bowl is 24.7 cm. Find the cost of polishing its outer surface at the rate of Rs. 4 per 100 cm2. (Take π = 3.14)
Sol. The outer radius of the bowl = (24.7 + 0.3) cm, i.e., R = 25 cm
∴ Total outer Surface area of the bowl = 2πr2 = 2 x 3.14 x (25)2 cm2
Cost of polishing the outer surface at the rate of Rs. 
Ex.5 Find the amount of water displaced by a solid spherical ball of diameter 28 cm.
Sol. Diameter = 28 cm
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FAQs on Surface area of Sphere and Hemisphere - Surface Areas and Volumes, Class 9, Mathematics - Extra Documents & Tests for Class 9
| 1. What is the formula for calculating the surface area of a sphere? |  |
Ans. The formula for calculating the surface area of a sphere is 4πr², where r represents the radius of the sphere.
| 2. How is the surface area of a hemisphere different from a sphere? | |
Ans. The surface area of a hemisphere is half of the surface area of a sphere. It can be calculated using the formula 2πr², where r is the radius of the hemisphere.
| 3. Can you explain the concept of surface area in simple terms? | |
Ans. Surface area refers to the total area of all the faces or surfaces of a three-dimensional object. It is measured in square units and helps us understand how much space the object occupies externally.
| 4. How can the surface area of a sphere be useful in real-life applications? | |
Ans. The surface area of a sphere has several practical applications. For example, it can be used to calculate the amount of paint needed to cover a spherical object, estimate the heat transfer rate for a heated or cooled sphere, or determine the amount of material required to create a spherical container.
| 5. Is there a relationship between the radius and the surface area of a sphere? | |
Ans. Yes, there is a direct relationship between the radius and the surface area of a sphere. As the radius increases, the surface area also increases. Conversely, if the radius decreases, the surface area decreases as well. This relationship can be mathematically expressed through the formula for the surface area of a sphere, which includes the radius as a variable.
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