Question
A right angled triangle whose sides are 3cm, 4cm and 5cm is revolved about the sides containing the right angle in two ways. Find the difference in volumes of the two cones so formed. Also, find their curved surfaces.
✓
Answer
We consider the following figure as follows
Let the angle B is right angle and the sides of the triangle are AB = 4cm, BC = 3cm,
AC = 5cm.
When the triangle is revolved about the side AB, then the base-radius, height and slant height of the produced cone becomes BC, AB and AC respectively. Therefore, the volume of the produced cone is
$\text{V}_1=\frac{1}{3}\pi\times\text{BC}^2\times\text{AB}$
$=\frac{1}{3}\pi\times(3)^2\times4$
$=12\pi$ cubic cm
In this case, the curved surface area of the cone is
$\text{S}_1=\pi\times\text{BC}\times\text{AC}$
$=\pi\times3\times5$
$=15\pi$ square cm
When the triangle is revolved about the side BC, then the base-radius, height and slant height of the produced cone becomes AB, BC and AC respectively. Therefore, the volume of the produced cone is
$\text{V}_2=\frac{1}{3}\pi\times\text{AB}^2\times\text{BC}$
$=\frac{1}{3}\pi\times(4)^2\times3$
$=16\pi$ cubic cm
Let the angle B is right angle and the sides of the triangle are AB = 4cm, BC = 3cm,
AC = 5cm.
When the triangle is revolved about the side AB, then the base-radius, height and slant height of the produced cone becomes BC, AB and AC respectively. Therefore, the volume of the produced cone is
$\text{V}_1=\frac{1}{3}\pi\times\text{BC}^2\times\text{AB}$
$=\frac{1}{3}\pi\times(3)^2\times4$
$=12\pi$ cubic cm
In this case, the curved surface area of the cone is
$\text{S}_1=\pi\times\text{BC}\times\text{AC}$
$=\pi\times3\times5$
$=15\pi$ square cm
When the triangle is revolved about the side BC, then the base-radius, height and slant height of the produced cone becomes AB, BC and AC respectively. Therefore, the volume of the produced cone is
$\text{V}_2=\frac{1}{3}\pi\times\text{AB}^2\times\text{BC}$
$=\frac{1}{3}\pi\times(4)^2\times3$
$=16\pi$ cubic cm
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Prove that both the roots of the equation $(x - a)(x - b) + (x - b)(x - c) + (x - c)(x - a) = 0 $are real but they are equal only when $a = b = c.$
→As deduced from a survey, the classification of skilled workers is shown in the pie diagram . If the number of workers in the production sector is 4500, answer the following questions.
(i) What is the total number of skilled workers in all fields?
(ii) What is the number of skilled workers in the field of constructions?
(iii) How many skilled workers are in agriculture?
(iv) Find the difference between the numbers of workers in the field of production and construction.
The length of a rectangle is thrice as long as the side of a square. The side of the square is $4\ cm$ more than width of a the rectangle. Their areas being equal, find their dimensions.
→Two different dice are rolled simultanceously. Find the probability that the sum of the numbers on the two dice is 10.
A wire is bent to form a square enclosing an area of $484m^2$. Using the same wire, a circle is formed. Find the area of the circle.
→In the given figure, from the top of a solid cone of height $12\ cm$ and base radius $6\ cm$, a cone of height $4\ cm$ is removed by a plane parallel to the base. Find the total surface area of the remaining solid.$\Big(\text{use}\ \pi=\frac{22}{7}\text{and}\sqrt{5}=2.236\Big).$
→A mixer manufacturing company manufactured 600 mixers in 3rd year and in 7th year they manufactured 700 mixers. If every year there is same growth in the production of mixers then find (i) Production in the first year (ii) Production in 10th year (iii) Total production in first seven years.
Obtain all zeros of $f(x) = x^3 + 13x^2 + 32x + 20$, if one of its zeros is $-2.$
→Mr.Jitendra invested an equal amount in two companies by purchasing equity shares with market price Rs. 160 and Rs.175 each. At the end of the year, both the companies declared the dividend of 15% and 20% each. In which company was her investment profitable?
Find the term of the arithmetic progression $9,12,15,18, \ldots .$. which is 39 more than its $36^{\text {th }}$ term.
→