Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > Very Short Answer Type Questions: Surface Areas & Volumes
Class 9 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Q1. What is the longest pole that can be put in a room of dimensions l = 10 cm, b = 10 cm and h = 5 cm?
Ans: The longest diagonal of a cuboid =
∴ The length of the required pole (diagonal) = 
Q2. The total surface area of a cube is 96 cm2. What is its volume?
Ans: Total surface area of the cube = 6l2
∴ 
Thus, the volume of the cube = l3 = 43 = 64 cm3
Q3. The radius of a sphere doubled. What percent of its volume is increased?
Ans: Original volume = (4/3)πr3
Increased volume = (4/3)π(2r)3 = 32/3πr3
Increase in volume = 32/3πr3 - 4/3πr3 = 28/3πr3
∴ Percent increase in volume = 
Q4. Write ‘True or False’ for the following statements: (i) A right circular cylinder just encloses a sphere of radius r as shown in the figure. The area of the sphere is equal to the curved surface area of the cylinder.
Ans: True.
∵ [Radius of the sphere] = [Radius of the cylinder] = r
∴ The diameter of the sphere = 2r
⇒ Height of the cylinder (h) = 2r
Now, the surface area of the sphere = 4πr2
And curved surface area of the cylinder = 2πrh = 2πr (2r) = 4πr2
(ii) An edge of a cube measures ‘r’ cm. If the largest possible right circular cone is cut out of this cube, then the volume of the cone (in cm3) is 1/6πr3
Ans: False.
∵ Height of the cone = r cm
∴ The diameter of the base of the cone = r cm
⇒ Radius of the base of the cone = (r/2) cm
Now volume of the cone 
Q5. If the total surface area of a sphere is 154 cm2. Find its total volume.
Ans: Let ‘r’ be the radius of the sphere
∴ Total S.A. = 4 π r2 = 154 cm2
or 
Now, 
Q6. If the radius of a sphere is 3r then what is its volume?
Ans:
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FAQs on Class 9 Maths Chapter 11 Question Answers - Surface Areas and Volumes
| 1. What is the difference between surface area and volume? |  |
Ans.Surface area measures the total area of all the surfaces of a three-dimensional object, while volume measures the amount of space the object occupies. Surface area is typically measured in square units, while volume is measured in cubic units.
| 2. How do you calculate the surface area of a cylinder? | |
Ans.To calculate the surface area of a cylinder, you use the formula: Surface Area = 2πr(h + r), where r is the radius of the base and h is the height of the cylinder. This formula accounts for the area of the two circular bases and the rectangular side that wraps around the cylinder.
| 3. What formulas are used for finding the volume of common shapes like cubes and spheres? | |
Ans.For a cube, the volume is found using the formula: Volume = a³, where a is the length of a side. For a sphere, the volume is calculated using the formula: Volume = (4/3)πr³, where r is the radius of the sphere.
| 4. Why is it important to understand surface areas and volumes in real life? | |
Ans.Understanding surface areas and volumes is essential in various real-life applications, such as construction, manufacturing, and packaging. It helps in determining materials needed, optimizing space, and ensuring proper design for functionality.
| 5. How can I apply the concepts of surface area and volume in everyday situations? | |
Ans.You can apply these concepts in everyday situations such as calculating how much paint is needed to cover a wall (surface area) or determining how much water a swimming pool can hold (volume). Understanding these concepts helps in making informed decisions in home improvement and other practical scenarios.
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