NCERT Solutions Class 10 Maths Chapter 13 – Surface Areas and Volumes Exercise 13.1

NCERT Solutions for Class 10 Maths Chapter 13 – Surface Areas and Volumes Exercise 13.1 are designed to help students understand the concepts of surface area and volume of 3D figures such as cylinders, cones, spheres, and hemispheres. This exercise will help students apply formulas to calculate the surface area and volume of various solid shapes.

NCERT Solutions Class 10 Maths Chapter 13 – Surface Areas and Volumes Exercise 13.1

Surface Areas and Volumes

Medium

Q.

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

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Surface Areas and Volumes

Medium

Q.

A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see the following figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

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Surface Areas and Volumes

Medium

Q.

From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm².

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Surface Areas and Volumes

Medium

Q.

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the following figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.

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Surface Areas and Volumes

Medium

Q.

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.

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Surface Areas and Volumes

Medium

Q.

Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)

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Surface Areas and Volumes

Medium

Q.

A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm (see the following figure)

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Exercise 13.1 focuses on:

• Calculating surface area and volume of cylinder, cone, and sphere.

• Applying the surface area and volume formulas in real-world problems.

• Understanding the relationship between radius, height, and surface area/volume in solids.

These solutions are presented in a step-by-step manner, making it easier for students to understand the geometric principles and solve problems effectively for Class 10 exams.

NCERT Solutions for Class 10 Maths Chapter 13 – Surface Areas and Volumes Exercise 13.1 are designed to help students understand the concepts of surface area and volume of 3D figures such as cylinders, cones, spheres, and hemispheres. This exercise will help students apply formulas to calculate the surface area and volume of various solid shapes.

Exercise 13.1 focuses on:

• Calculating surface area and volume of cylinder, cone, and sphere.

• Applying the surface area and volume formulas in real-world problems.

• Understanding the relationship between radius, height, and surface area/volume in solids.

These solutions are presented in a step-by-step manner, making it easier for students to understand the geometric principles and solve problems effectively for Class 10 exams.

FAQs: Class 10 Maths Chapter 13 – Surface Areas and Volumes Exercise 13.1

Q1. What is the focus of Exercise 13.1?
Answer:
Exercise 13.1 focuses on calculating the surface area and volume of solid figures like cylinders, cones, and spheres using the appropriate formulas.

Q2. What are the formulas for surface area and volume in this exercise?
Answer:
Here are the key formulas:

• Surface Area of a Cylinder:

  $\text{Surface Area} = 2\pi r(h + r)$Surface Area=2πr(h+r),
  where

  $r$r is the radius and

  $h$h is the height.

• Volume of a Cylinder:

  $V = \pi r^2 h$V=πr2h

• Surface Area of a Cone:

  $\text{Surface Area} = \pi r(l + r)$Surface Area=πr(l+r),
  where

  $l$l is the slant height.

• Volume of a Cone:

  $V = \frac{1}{3} \pi r^2 h$V=31​πr2h

• Surface Area of a Sphere:

  $\text{Surface Area} = 4\pi r^2$Surface Area=4πr2

• Volume of a Sphere:

  $V = \frac{4}{3} \pi r^3$V=34​πr3

Q3. How do I calculate the surface area of a cylinder?
Answer:
The surface area of a cylinder is given by:

$$\text{Surface Area} = 2\pi r(h + r)$$

Surface Area=2πr(h+r)

where

$r$

r is the radius of the base and

$h$

h is the height of the cylinder. This formula includes the areas of both circular bases and the curved surface.

Q4. How do I calculate the volume of a cone?
Answer:
The volume of a cone is calculated by the formula:

$$V = \frac{1}{3} \pi r^2 h$$

V=31​πr2h

where

$r$

r is the radius of the base and

$h$

h is the height of the cone.

Q5. How do NCERT Solutions help with exam preparation?
Answer:
NCERT Solutions provide step-by-step explanations for calculating surface area and volume of 3D figures. By practicing these problems, students can strengthen their understanding of the concepts and apply formulas correctly in Class 10 exams.

FAQs: Class 10 Maths Chapter 13 – Surface Areas and Volumes Exercise 13.1

Q1. What is the focus of Exercise 13.1?
Answer:
Exercise 13.1 focuses on calculating the surface area and volume of solid figures like cylinders, cones, and spheres using the appropriate formulas.

Q2. What are the formulas for surface area and volume in this exercise?
Answer:
Here are the key formulas:

• Surface Area of a Cylinder:

  $\text{Surface Area} = 2\pi r(h + r)$Surface Area=2πr(h+r),
  where

  $r$r is the radius and

  $h$h is the height.

• Volume of a Cylinder:

  $V = \pi r^2 h$V=πr2h

• Surface Area of a Cone:

  $\text{Surface Area} = \pi r(l + r)$Surface Area=πr(l+r),
  where

  $l$l is the slant height.

• Volume of a Cone:

  $V = \frac{1}{3} \pi r^2 h$V=31​πr2h

• Surface Area of a Sphere:

  $\text{Surface Area} = 4\pi r^2$Surface Area=4πr2

• Volume of a Sphere:

  $V = \frac{4}{3} \pi r^3$V=34​πr3

Q3. How do I calculate the surface area of a cylinder?
Answer:
The surface area of a cylinder is given by:

$$\text{Surface Area} = 2\pi r(h + r)$$

Surface Area=2πr(h+r)

where

$r$

r is the radius of the base and

$h$

h is the height of the cylinder. This formula includes the areas of both circular bases and the curved surface.

Q4. How do I calculate the volume of a cone?
Answer:
The volume of a cone is calculated by the formula:

$$V = \frac{1}{3} \pi r^2 h$$

V=31​πr2h

where

$r$

r is the radius of the base and

$h$

h is the height of the cone.

Q5. How do NCERT Solutions help with exam preparation?
Answer:
NCERT Solutions provide step-by-step explanations for calculating surface area and volume of 3D figures. By practicing these problems, students can strengthen their understanding of the concepts and apply formulas correctly in Class 10 exams.