Download App

Volume and Surface area of Solids — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsVolume and Surface area of Solids5 Marks
Question
A solid rectangular block of dimensions 4.4m, 2.6m and 1m is cast into a hollow cylindrical pipe of internal radius 30cm and thickness ​5cm. Find the length of the pipe.
✓

Answer

We have,
Length of the rectangular block, l = 4. 4m,
Breadth of the rectangular block, b = 2. 6m,
Height of the rectangular block, h = 1m,
Internal radius of the cylindrical pipe, r = 30cm = 0. 3m and
Thickness of the pipe = 5cm = 0. 05m
Also, the external radius of the pipe = 0. 3 + 0. 05 = 0. 35m
Let the length of the pipe be H.
Now,
Volume of the pipe = Volume of the block
$\Rightarrow\pi\text{R}^2\text{H}=\pi\text{r}^2\text{H}=\text{lbh}$
$\Rightarrow\pi(\text{R}^2-\text{r}^2)\text{H}=\text{lbh}$
$\Rightarrow\frac{22}{7}\times(0.35^2-0.3^2)\text{H}=4.4\times2.6\times1$
$\Rightarrow\frac{22}{7}\times(0.1225-0.09)\text{H}=4.4\times2.6$
$\Rightarrow\frac{22}{7}\times0.0325\times\text{H}=4.4\times2.6$
$=\text{H}=\frac{4.4\times2.6\times7}{22\times0.0325}$
$\therefore\text{H}=112\text{m}$
So, the length of the pipe is 112m.

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 "5 Marks Question" from Volume and Surface area of Solids→Volume and Surface area of Solids — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

Solve the following quadratic equation:
$\frac{1}{\text{2a}+\text{b}+\text{2x}}=\frac{1}{\text{2a}}+\frac{1}{\text{b}}+\frac{1}{\text{2x}}$
→
If $\sec\theta=\frac{5}{4},$ show that $\frac{\big(\sin\theta-2\cos\theta\big)}{\big(\tan\theta-\cot\theta\big)}=\frac{12}{7}.$
→
Each of the equal sides of an isosceles triangle measures 2cm more than its height, and the base of the triangle measures 12cm. Find the area of the triangle.
→
Find a cubic polynomial whose zeroes are $\frac{1}{2},$ $1$ and $−3$.
→
If three times the larger of two numbers is divided by the smaller, we get 4 as the quotient and 8 as the remainder. If five times the smaller is divided by the larger, we get 3 as the quotient and 5 as the remainder. Find the numbers.
→
How many three-digit natural numbers are divisible by $9$?
→
The frequency distribution table of more than type is as follows:
Production yield (kg/ha) (lower class limits) Cumulative frequency (cf)
More than 50 2 + 98 = 100
More than 55 8 + 90 = 98
More than 60 12 + 78 = 90
More than 65 24 + 54 = 78
More than 70 38 + 16 = 54
More than 75 16
Taking the lower class limits on x-axis and their respective cumulative frequencies on y-axis, its ogive can be obtained as follows:
→
Draw two tangents to a circle of radius 3.5cm from a point P at a distance of 6.2cm from its centre.
→
If one zero of the polynomial $p(x) = x^3 - 6x^2 + 11x - 6$ is $3$, find the other two zeroes.
→
To construct a triangle similar to $\triangle\text{ABC}$ in which BC = 4.5cm, $\angle\text{B}=45^\circ$ and $\angle\text{C}=60^\circ,$ using a scale factor of $\frac35$ BC will be divided in the ratio.
  1. 3 : 4
  2. 4 : 7
  3. 3 : 10
  4. 3 : 7
→