Download App

Surface Areas And Volumes — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsSurface Areas And Volumes3 Marks
Question
A solid is in the form of a cylinder with hemispherical ends. Total height of the solid is $19\ cm$ and the diameter of the cylinder is $7\ cm$. Find the volume and total surface area of the solid.
✓

Answer

Volume of cylinder $=\pi\text{r}^2\text{h}$
$=\frac{22}{7}\times\frac{7}{2}\times\frac{7}{2}\times12$
$=462\text{cm}^3$
Volume of 2 hemisphere $=4\pi\text{r}^3$
$=\frac{4}{3}\times\frac{22}{2}\times\frac{7}{2}\times\frac{7}{2}\times\frac{7}{2}$
$=179.6\text{cm}^3$
Therefore,
Volume of solid $= 462 + 179.6$
$= 641.6\ cm^3$
Total surface area of the solid
$=2\pi\text{rh}+4\pi\text{r}^2$
$=2\pi\text{r}(\text{h}+2\text{r})$
$=2\times\frac{22}{7}\times\frac{7}{2}\Big(12+2\times\frac{7}{2}\Big)$
$=418\text{cm}^2$

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 "3 Marks Question" from Surface Areas And Volumes→Surface Areas And Volumes — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

The base radii of two right circular cones of the same height are in the ratio 2 : 3. Find ratio of their volumes.
→
From the railway station I took a rickshaw to go home. It is decided that I have to pay Rs. X for the first kilometre and for each kilometre Rs. Y for the next. For 10 kilometres the fare is Rs. 40 and for 16 kilometres fare is Rs. 58. Find the fare for the first kilometre.
→
What is the ratio of the volume of a cube to that of a sphere which will fit inside it?
→
Find the mass of a $3.5\ m$ long lead pipe, if the external diameter of the pipe is $2.4\ cm$, thickness of the metal is 2mm and the mass of $1\ cm^3$​​​​​​​ of lead is $11.4\ g$.
→
Determine the set of values of k for which the given following quadratic has real root:
$2x^2 + kx - 4 = 0$
→
Neel has invested in shares as follows. Find his total investment.
Company A : 350 shares, FV = ₹ 10, premium = ₹ 7
Company B : 2750 shares, FV = ₹ 5, Discount = ₹ 1.
Company C : 50 shares, FV = ₹ 100, MV = ₹ 150.
→
All integers between $1$ and $500$ which are multiplies of $2$ as well as of $5$.
→
A two digit number is to be formed from the digits 2, 3, 5 without repetition of the digits. Complete the following activity to find the probability that the number so formed is an odd number.
Activity :
Let S be the sample space.
$\therefore S=\{23,25,32,$ ⬜, $52,53\} $
$\therefore n(S)=$ ⬜
Event A : The number so formed is an odd number.
$\therefore A=\{23,25, $ ⬜, $53\} $
$\therefore n(A)=4 $
$\therefore P(A)=\frac{⬜}{n(S)} ...... ..(\text {Formula}) $
$\therefore P(A)=\frac{⬜}{6} $
$\therefore P(A)=\frac{⬜}{3} .$
→
Area of a sector of a circle of radius 15 cm is $30 cm^2$. Find the length of the arc of the sector.
→
If the $n^{th}$​​​​​​​ term of a progression is $(4n - 10)$ show that it is an AP. Find its:
  1. First term.
  2. Common difference.
  3. $16^{th}$​​​​​​​ term.
→