Class 10 Exam  >  Class 10 Notes  >  Mathematics (Maths) Class 10  >  Very Short Answer Questions: Surface Areas & Volumes

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

Q1: The radii for the top as well as the bottom of a bucket for the slant height of 45 cm are 28 cm and 7 cm, respectively. The curved surface area of the bucket is?

Ans: Slant height of the bucket = 45 cm

Top radius is = r1 = 28cm 

Bottom radius is = r2 = 7cm 

Curved surface area of the bucket is = πl(r1+r2)  

=22/7 * 45 * (28+7)

= 22/7 *45 *35

=4950cm2      

Q2. If two identical solid cubes of side ‘x’ are joined end to end, then the total surface area of the resulting cuboid is 12x2. Is it true?  

Ans: ∵ The total surface area of a cube of side x is 6x2
When they are joined end to end, the length becomes 2x
∴Total surface area
= 2[lh + bh + hl]

= 2 [(2x · x) + (x · x) + (2x · x)]

= 2 [2x2 + x2 + 2x2]

= 2 [5x2] = 10x2 ≠ 12x2
∴ False   

Q3. If a solid cone of base radius ‘r’ and height ‘h’ is placed over a solid cylinder having same base radius ‘r’ and height ‘h’ as that of the cone, then the curved surface area of the shape is Is it true?

Ans: ∵ Curved surface area of a cone Class 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes 

And curved surface area of the cylinder = 2πrh
∴ The curved surface area of the combinationClass 10 Maths Chapter 11 Question Answers - Surface Areas and Volumes

∴ True.

Q4. A cylinder and a cone are of the same base radius and same height. Find the ratio of the volumes of the cylinder of that of the cone.

Ans: Let the base radius = r and height = h

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

⇒ The required ratio = 3: 1

Q5:  If two solid hemispheres for the same base radius r are joined together along with their bases, what is the curved surface area of this new solid?

Ans: The radius of the hemisphere = r

We know curved surface area = 2πr2  

The curved surface area of two solid hemisphere

= 2 * 2πr2

= 4πr2  

Q6: Vol. and surface area of a solid hemisphere are numerically equal. What is diameter of hemisphere?

Ans:

Vol. of hemisphere = S. A. of solid hemisphere 2 ,

⇒ 23πr2 = 3πr2

⇒ r = 92

∴ diameter = 2r = 9 units

Q7: Volumes for two spheres are in the ratio 64: 27. The ratio for their surface areas is?

Ans: Assume two-sphere having radius r1 and r2

As per the question, 

volume of the first sphere / volume of the second sphere = 64/27

= (4/3 *πr13)/ (4/3 *πr23) = 64/27

(r1/r2)3 = 64/27

r1/r2 = 3√(64/27) =4/3

Ratio for their surface area is = (4 *πr12)/ (4 *πr22) = r12/r22 = (r1/r2)2 = (4 /3)2 = 16/9

 So, the required ratio is 16:9

Q8: Two cones have their heights in the ratio 1 : 3 and radii in the ratio 3 : 1. What is the ratio of their volumes?

Ans: Given,

Ratio of heights of two cones = 1 : 3

Ratio of radii = 3 : 1

Let h and 3h be the height of two cones.

Also, 3r and r be the corresponding radii of cones.

So, r1 = 3r, h1 = h, r2 = r, h2 = 3h.

Ratio of volumes = [(1/3)πr12h1]/ [(1/3)πr22h2]

= [(3r)2 h]/[r2 (3h)] = (9r2h)/(3r2h)

= 3/1

Hence, the ratio of volumes = 3:1

     

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 calculating the surface area of a sphere?
Ans.The surface area of a sphere is calculated using the formula \(4\pi r^2\), where \(r\) is the radius of the sphere.
2. How do you find the volume of a cylinder?
Ans.The volume of a cylinder can be found using the formula \(V = \pi r^2 h\), where \(r\) is the radius of the base and \(h\) is the height of the cylinder.
3. What is the difference between surface area and volume?
Ans.Surface area refers to the total area that the surface of an object occupies, while volume measures the space that an object occupies. They are different concepts and are measured in different units.
4. How can I calculate the surface area of a rectangular prism?
Ans.The surface area of a rectangular prism can be calculated using the formula \(SA = 2(lw + lh + wh)\), where \(l\), \(w\), and \(h\) are the length, width, and height of the prism, respectively.
5. What is the formula for the volume of a cone?
Ans.The volume of a cone is calculated using the formula \(V = \frac{1}{3} \pi r^2 h\), where \(r\) is the radius of the base and \(h\) is the height of the cone.
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