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Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

Q1. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume is 1/27th of the volume of the given cone, at what height above the base is the section made?

Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

Sol. In the figure, we have ΔABC ~ ΔADE

[By AA similarity]

Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

[∵ corresponding sides of similar Δs are proportional.]

Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes     ...(1)
Here, volume of the small cone = Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Volume of the given cone =  Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Since, [Volume of the small cone] = 1/27
[Volume of the given cone]

Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

∴The required height BD = AD − AB = (30 − 10) cm = 20 cm


Q2. A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and slant height of the conical portion is 53 m, find the area of the canvas needed to make the tent.  [Use π = 22/7]

Sol. For cylindrical part:

We have, radius (r) = 52.5 m
Height (h)=3 m
Curved surface area = 2πrh
For the conical part
Slant height (l) = 53 m
Radius (r) = 52.5 m
∴Curved surface area = πrl
Area of the canvas = 2πrh + πrl
= πr (2h + l)

  Class 10 Maths Chapter 11 Question Answers - Surface Areas and VolumesClass 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

= 11 × 15 × 59 m2 =  9735 m2


Q3. An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of the base of each of cone and cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part in 36 cm high. Find the weight of the pillar if one cu. cm of iron weighs 7.8 grams.

Sol. Here, height of the cylindrical part h = 240 cm
Height of the conical part, H = 36 cm
Radius r =8 cm
Now, the total volume of the pillar

Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes


Q4. A building is in the form of a cylinder surmounted by a hemispherical dome as shown in the figure. The base diameter of the dome is equal to 2/3 of the total height of the building. Find the height of the building, if it contains  Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes of air.

Sol. Here, radius of the hemispherical part = r (say)

Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

Let the total height of the building = h
And the height of the cylindrical part = H

Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

Class 10 Maths Chapter 11 Question Answers - Surface Areas and VolumesClass 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
But, volume of the air in the building

Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

Thus, the required height of the building is 6 metres.


Q5. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 4 cm and diameter of the base is 8 cm. Determine the volume of the toy. If the cube circumscribes the toy, then find the difference of the volumes of the cube and the toy. Also, find the total surface area of the toy.

Sol. Let the radius of the hemisphere = r
And height of the cone = h

Class 10 Maths Chapter 11 Question Answers - Surface Areas and VolumesClass 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

Since, the cube circumscribing the given solid must have its edge as (4 + 4) cm i.e., 8 cm,
∴ Volume of the cube =(edge)3 = (8)3 cm3 = 512 cm3
Now, the difference in volumes of the cube and the toy

Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Also, total surface area of the toy

Class 10 Maths Chapter 11 Question Answers - Surface Areas and VolumesClass 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes
Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

The document Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes is a part of the Class 10 Course Mathematics (Maths) Class 10.
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FAQs on Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

1. What is the formula for finding the surface area of a cube?
Ans. The formula for finding the surface area of a cube is 6 times the square of its side length. So, if the side length of a cube is 'a', then the surface area is given by 6a^2.
2. How do you calculate the volume of a cylinder?
Ans. The volume of a cylinder can be calculated by multiplying the area of its base (which is a circle) by its height. So, if the radius of the circular base is 'r' and the height is 'h', then the volume of the cylinder is given by πr^2h.
3. What is the difference between lateral surface area and total surface area of a cone?
Ans. The lateral surface area of a cone refers to the curved surface area excluding the base, while the total surface area includes the curved surface area as well as the base(s). The lateral surface area of a cone can be calculated using the formula πrl, where 'r' is the radius of the base and 'l' is the slant height.
4. How do you find the volume of a sphere?
Ans. The volume of a sphere can be calculated using the formula (4/3)πr^3, where 'r' is the radius of the sphere. This formula represents the amount of space occupied by the sphere.
5. Can you explain how to find the surface area of a triangular pyramid?
Ans. To find the surface area of a triangular pyramid, you need to calculate the sum of the areas of its triangular faces. The formula for finding the area of a triangle is (1/2)base×height. So, for each triangular face, multiply the base length by the corresponding height and divide it by 2. Finally, add up the areas of all the triangular faces to get the total surface area of the pyramid.
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