Download App

Mensuration — MATHS STD 10 — Question

Tamilnadu BoardEnglish MediumSTD 10MATHSMensuration2 Marks
Question
A right-angled triangle whose sides are 6 cm, 8 cm and 10 cm is revolved about the sides containing the right angle in two ways. Find the difference in volumes of the two solids so formed.
✓

Answer

Three sides of a triangle are $6 cm , 8 cm$ and $10 cm$.
Case (i): If the triangle is revolved about the side $6 cm$, the cone will be formed with radius 6 $cm$ and height $8 cm$.

Volume of the cone $=\frac{1}{3} \pi r ^2 h$ cu. units
$
\begin{aligned}
& =\frac{1}{3} \times \pi \times 6 \times 6 \times 8 \\
& =96 \pi cm ^3
\end{aligned}
$

Case (ii): If the triangle is revolved about the side $8 cm$, the cone will be formed with radius 8 $cm$ and height $6 cm$.

Volume of the cone $=\frac{1}{3} \times \pi \times 8 \times 8 \times 6$
$
=128 \pi cm ^3
$
Difference in volume of the two solids
$
\begin{aligned}
& =(128 \pi-96 \pi) cm ^3 \\
& =32 \pi cm ^3
\end{aligned}
$
$
\begin{aligned}
& =32 \times \frac{22}{7} cm ^3 \\
& =100.57 cm ^3
\end{aligned}
$
The difference in the volume of the two solids $=100.57 cm ^3$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[2 Mark Questions]" from Mensuration→Mensuration — all question types→MATHS STD 10 question papers→Tamilnadu Board STD 10 question papers→Tamilnadu Board question paper generator→

Similar questions

Find the square root of the following rational expression
$
\frac{7 x^2+2 \sqrt{14} x+2}{x^2-\frac{1}{2} x+\frac{1}{16}}
$
→
Find the equation of a line whose inclination is 30˚ and making an intercept – 3 on the Y-axis.
→
You are downloading a song. The percent y (in decimal form) of megabytes remaining to get downloaded in x seconds is given by y = – 0.1x + 1 after how many seconds the song will be downloaded completely?
→
Check whether the given lines are parallel or perpendicular
5x + 23y + 14 = 0 and 23x – 5x + 9 = 0
→
Determine the quadratic equation, whose sum and product of roots are $\frac{5}{3}, 4$
→
A cat is located at the point(– 6, – 4) in xy plane. A bottle of milk is kept at (5, 11). The cat wish to consume the milk travelling through shortest possible distance. Find the equation of the path it needs to take its milk.
→
A conical flask is full of water. The flask has base radius r units and height h units, the water is poured into a cylindrical flask of base radius xr units. Find the height of water in the cylindrical flask.
→
Prove that $\cot ^2 A \left[\frac{\sec A -1}{1+\sin A }\right]+\sec ^2 A \left[\frac{\sin A -1}{1+\sec A }\right]=0$
→
A bag contains 12 blue balls and x red balls. If one ball is drawn at random what is the probability that it will be a red ball?
→
Construct a $3 \times 3$ matrix whose elements are given by $a_{i j}=\frac{( i + j )^3}{3}$
→