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The slant height of a frustum of a cone is 4 cm and the perimeters circumference of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum. Let the slant height of the frustum be l and radius of the both ends of the frustum be r1 and r2.
A fez, the cap used by the turks, is shaped like the frustum of a cone see figure. If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it. Let the slant height of fez be l and the radius of upper end which is closed be r1 and the other end which is open be r2. A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively.
Also find the cost of metal sheet used to make the container. Let h be the height of the container, which is in the form of a frustum of a cone whose lower end is closed and upper end is opened.
Also, let the radius of its lower end be r1 and upper end be r2. Let r1 and r2 be the radii of the frustum of upper and lower ends cut by a plane. A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm and diameter 10 cm, so as to cover the curved surface of the cylinder.
Find the length and mass of the wire, assuming the density of copper to be 8. When a wire is one round wound about a cylinder, it covers a 3 mm of length of the cylinder. A right triangle, whose sides are 3 cm and 4 cm other than hypotenuse is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. Porous bricks are placed in the water until the cistern is full to the brim.
Each brick absorbs one-seventeenth of its own volume of water. In one fortnight of a given month, there Byjus Class 10 Maths Triangles Vol was a rainfall of 10 cm in a river valley. If the area of the valley is km 2 , show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each km long, 75 m wide and 3 m deep.
An oil funnel made of tin sheet consists of a 10 cm long Ch 5.3 Maths Class 10 Zoom cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel. Given, oil funnel is a combination of a cylinder and a frustum of a cone. Derive the formula for the curved surface area and total surface area of the frustum of a cone.
Using the symbols as explained. We complete the conical part OCD. Let slant height of the cone OAB be l 1 and its height be h 1 i. Derive the formula for the volume of the frustum of a cone given to you in the section Let the height of the cone OAB be h 1 and its slant height be l 1. Chapter 13 Class 10 Maths NCERT Solutions plays very important role during the preparation of board exams as a lot of questions from this topic can be asked.
There are total 5 topics in this chapter which will guide students in a better way. We are going to learn about how to find surface areas and volumes of these types of objects. The total surface area of the new solid is the sum of the curved surface areas of each of the individual parts.
The volume of the solid formed by joining two basic solids will be the sum of the volumes of the constituents. In this topics, we will dealing with the questions based on finding the volume of a frustum of a cone. How many exercises in Chapter 13 Surface Areas and Volumes There are total 5 exercise in the Chapter 13 Surface Areas and Volumes which will make students while solving any questions. These are also useful for competitive exams and higher grades. What do you mean by Cube? Find the sum of the first 40 positive integers divisible by 6.
Find the sum of the first 15 multiples of 8. Find the sum of the odd numbers between 0 and How much money the contractor has to pay as penalty, if he has delayed the work by 30 days? In a school, students thought of planting trees in and around the school to reduce air pollution.
It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, eg. There are three sections of each class. How many trees will be planted by the students? A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.
What is the total length of such a spiral made up of thirteen consecutive semicircles? This means that according to the formula, we can say that:.
It should also be noted by students who refer to the NCERT Class 10 Maths Chapter 5 Solutions that the finite portion of an arithmetic progression is known as finite arithmetic progression. This means that the sum of a finite AP is known as an arithmetic series.
The behaviour of the entire sequence will also depend on the values of the common difference. This means that if the value of the common difference is positive, then the member terms will grow towards positive infinity. And if the value of the common difference is negative, then the member terms will move towards negative infinity.
One can easily calculate the sum of n terms of any known progression. For an arithmetic progression, it is possible to calculate the sum of the first n terms if the value of the first term and the total terms are known. The formula is mentioned below. But what if the value of the last term of the arithmetic progression is given?
In that case, students should use the formula that is mentioned below. For ease of revision, we have also summarized all the major formulas of this chapter in a table. That table is mentioned below. General Form of AP. The nth term of AP. Sum of n terms in AP. Sum of all terms in a finite AP with the last term as I.
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Some of those benefits are:. All answers are written according Class 10 Maths Ch 5 Ex 5.3 Time to the guidelines set by CBSE. Questions are solved by the best academic experts in India. Every solved answer has an explanation section. This section explains the thought process that the academic expert engaged in to arrive at the final answer.
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