Question
The given figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other. Find the volurne of the solid.
✓
Answer
Height of cylinder $= 6.5\ cm$
height of cone $= h_2$ =$ (12.8 - 6.5)cm = 6.3cm$
Radius of cylinder = radius of cone
= radius of hemisphere
$=\Big(\frac{7}{2}\Big)\text{cm}$
Volume of solid = volume of cylinder + volume of cone + volume of hemisphere
$=\pi\text{r}^2\text{h}_1+\frac{1}{3}\pi\text{r}^2\text{h}_2+\frac{2}{3}\pi\text{r}^2\Big(\text{h}_1+\frac{1}{3}\text{h}_2+\frac{2}{3}\text{r}\Big)$
$=\Big[\frac{22}{7}\times3.5\times3.5\times\Big(6.5+6.3\times\frac{1}{3}+\frac{2}{3}\times3.5\Big)\Big]$
$=[(38.5)\times(6.5+2.1+2.33)]\text{cm}^3$
$=(38.5\times10.93)\text{cm}^3=420.80\text{cm}^3$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The sum of the radii of two circles is 7cm, and the differece of their circumferences is 8cm. Find the circumferences of the circleas.$\Big[\text{Use }\pi=\frac{22}{7}\Big]$
→In $\Delta$PQR, ray QS bisects $\angle$PQR. P-S-R. Show that $\frac{ A (\Delta PQS )}{ A (\Delta QRS )}=\frac{ PQ }{ QR }$.
→If One coin and one die are thrown simultaneously, find the probability of the following events.
i) Event A : To get a tail and an even number.
ii) Event B: To get head and an odd number.
i) Event A : To get a tail and an even number.
ii) Event B: To get head and an odd number.
The length of three concesutive sides of a quadilateral circumscribing a circle are 4cm, 5cm, 7cm respectively. Determine the length of thefourth side.
Two A.P.s have the same common difference. The first term of one A.P. is $2$ and that of the other is $7$ . The difference between their $10^{\text {th }}$ terms is the same as the difference between their $21^{\text {st }}$ terms, which is the same as the difference between any two corresponding terms. Why?
→In $\triangle\text{ABC},\ \angle\text{C}$ is an obtuse angle. $\text{AD}\perp\text{BC}$ and $AB^2 = AC^2 + 3BC^2.$ Prove that $BC = CD.$
→How many terms are there in the A.P.?
$7, 13, 19, ....., 205.$
→$7, 13, 19, ....., 205.$
The diameter of a sphere is 42cm. It is melted and drawn into a cylindrical wire of diameter 2.8cm. Find the length of the wire.
Find the coordinates of the midpoint of the line segment joining P(0,6)and Q(12,20).
Show that the following numbers are irrational.
$\frac{1}{\sqrt{2}}$
→$\frac{1}{\sqrt{2}}$