Introduction – Surface Areas and Volumes (Exercise 13.1)

In Class 10 Math Ch Surface Areas and Volumes Ex 13.1, we explore the world of three-dimensional shapes and learn how to calculate their surface areas and volumes. Exercise 13.1 focuses specifically on finding surface areas of basic solid shapes like cuboids, cubes, cylinders, cones, and spheres. These problems help students apply formulas practically and visualize real-life objects mathematically. This exercise is designed to strengthen your understanding of how to work with curved surfaces and total surface areas using standard formulas. Solving these questions builds a strong foundation for geometry and measurement-related problems in higher classes and daily life.

Class 10 Math Ch Surface Areas and Volumes – Ex 13.1

Question 1.

2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
Solution:
Given:

  • Volume of each cube = 64 cm³
  • Since cube volume = side³
    So, side of each cube = ∛64 = 4 cm

Step 1: Understand the new shape

  • Two cubes of side 4 cm are joined end to end
  • So, the resulting shape is a cuboid with dimensions:
    Length = 4 + 4 = 8 cm
    Width = 4 cm
    Height = 4 cm

Step 2: Surface Area of a Cuboid

Formula:
Surface Area = 2 × (length × width + width × height + height × length)

Substitute:

= 2 × (8 × 4 + 4 × 4 + 4 × 8)
= 2 × (32 + 16 + 32)
= 2 × 80 = 160 cm²

✅ Final Answer:

The surface area of the resulting cuboid is 160 cm².

Ex 13.1 Class 10 Maths Question 2.
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
Solution:
NCERT Solutions for Class 10 Maths Chapter 13 Pdf Q2

Ex 13.1 Class 10 Maths Question 3.
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of the same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.
Solution:
Ex 13.1 Class 10 Maths NCERT Solutions Q3

Ex 13.1 Class 10 Maths Question 4.
A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.
Solution:
Exercise 13.1 Class 10 Maths NCERT Solutions PDF Q4

Ex 13.1 Class 10 Maths Question 5.
A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter d of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.
Solution:
Ch 13 Maths Class 10 Maths NCERT Solutions PDF Q5

Ex 13.1 Class 10 Maths Question 6.
A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.
Solution:
Chapter 13 Maths Class 10 NCERT Solutions PDF Q6

Ex 13.1 Class 10 Maths Question 7.
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per m2. (Note that the base of the tent will not be covered with canvas.)
Solution:
Ex 13.1 Class 10 Maths NCERT Solutions PDF Q7

📘 Math & Science Solutions by Class

🔹 Class 10

🔹 Class 9

🔹 Class 8

🔹 Class 7

🔹 Class 6

🔹 Class 12

🔹 Class 11

For the official Class 10 Mathematics Solutions, you can visit:

  1. NCERT Textbooks (for Class 10):
ncert resources