Question
How many spherical lead shots each of diameter $4.2\ cm$ can be obtained from a solid rectangular lead piece with dimensions $66cm \times 42cm \times 21cm.$
✓
Answer
Given that, lots of spherical lead of shots made from a solid rectangular lead piece.
$\therefore$ Number of spherical lead shots
$=\frac{\text{volume of solid rectangular lead piece}}{\text{volume of a spherical lead shot}}\ ...(\text{i})$
Also, given that diameter of a spherical lead shot i.e. sphere $= 4.2\ cm$
$\therefore$ Radius of a spherical lead shot,
$\text{r}=\frac{4.2}{2}=2.1\text{cm}[\therefore\text{radius}=\frac{1}{2}\text{diameter}]$
So, volume of a spherical lead shot i.e.
$\text{sphere}=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\times\frac{22}{7}\times(2.1)^3$
$=\frac{4}{3}\times\frac{22}{7}\times2.1\times2.1\times2.1$
$=\frac{4\times22\times21\times21\times21}{3\times7\times1000}$
Now, length of rectangular lead piece, $l = 66\ cm$
Breadth of rectangular lead piece, $b = 42\ cm$
Hieght of rectangular lead piece, $h = 21\ cm$
$\therefore$ Volume of a solid rectangular lead piece i.e.
cuboid =$ l \times b \times h = 66 \times 42 \times 21$
From Eq. $(i)$, Number of spherical lead, shots
$\frac{66\times42\times21}{4\times22\times21\times21\times21}\times3\times7\times1000$
$=\frac{3\times22\times21\times2\times21\times21\times1000}{4\times22\times21\times21\times21}$
$=3\times2\times250$
$=6\times250=1500$
Hence, the required number of spherical lead shots is $1500.$
$\therefore$ Number of spherical lead shots
$=\frac{\text{volume of solid rectangular lead piece}}{\text{volume of a spherical lead shot}}\ ...(\text{i})$
Also, given that diameter of a spherical lead shot i.e. sphere $= 4.2\ cm$
$\therefore$ Radius of a spherical lead shot,
$\text{r}=\frac{4.2}{2}=2.1\text{cm}[\therefore\text{radius}=\frac{1}{2}\text{diameter}]$
So, volume of a spherical lead shot i.e.
$\text{sphere}=\frac{4}{3}\pi\text{r}^3$
$=\frac{4}{3}\times\frac{22}{7}\times(2.1)^3$
$=\frac{4}{3}\times\frac{22}{7}\times2.1\times2.1\times2.1$
$=\frac{4\times22\times21\times21\times21}{3\times7\times1000}$
Now, length of rectangular lead piece, $l = 66\ cm$
Breadth of rectangular lead piece, $b = 42\ cm$
Hieght of rectangular lead piece, $h = 21\ cm$
$\therefore$ Volume of a solid rectangular lead piece i.e.
cuboid =$ l \times b \times h = 66 \times 42 \times 21$
From Eq. $(i)$, Number of spherical lead, shots
$\frac{66\times42\times21}{4\times22\times21\times21\times21}\times3\times7\times1000$
$=\frac{3\times22\times21\times2\times21\times21\times1000}{4\times22\times21\times21\times21}$
$=3\times2\times250$
$=6\times250=1500$
Hence, the required number of spherical lead shots is $1500.$
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
In the given figure, $\triangle\text{OAB}\sim\triangle\text{OCD}.$ If $AB = 8\ cm, BO = 6.4\ cm$, $OC = 3.5\ cm$ and $CD = 5\ cm$, find.
→- $OA$
- $DO$
In the given figure, given that $\triangle\text{ABC}\sim\triangle\text{PQR}$ and quad ABCD ∼ quad $PQRS$. Determine the value of $x, y, z$ in each case.
→
Find the second term and $n ^{\text {th }}$ term of an $A.P.$ whose $6^{\text {th }}$ term is $12$ and $8^{\text {th }}$ term is $22 .$
→Find the roots of the following equations, if they exist, by applying the quadratic formula:
$\sqrt3\text{x}^2-2\sqrt2\text{x}-2\sqrt3=0$
→$\sqrt3\text{x}^2-2\sqrt2\text{x}-2\sqrt3=0$
Taxi charges in a city consist of fixed charges and the remaining depending upon the distance travelled in kilometres. If a man travels $80\ km$, he pays $₹ 1,330$, and travelling $90\ km$, he pays $₹ 1,490$. Find the fixed charges and rate per km.
→Solve the following system of equations by the method of cross-multiplication:
$\frac{\text{x}}{\text{b}}=\frac{\text{y}}{\text{b}},$
$\text{ax}+\text{by}=\text{a}^2+\text{b}^2.$
→$\frac{\text{x}}{\text{b}}=\frac{\text{y}}{\text{b}},$
$\text{ax}+\text{by}=\text{a}^2+\text{b}^2.$
If $\theta=\frac{15}{8},$ find the value of the all T-ratios of $\theta.$
→A medicine capsule is in the shape of a cylinder with two hemipheres stuck to each of its ends. The length of the entire capsule is $14\ mm$ and the diameter of the capsule is $5\ mm$. Fin its surface area.
→A box contains 3 blue, 2 white, and 4 red marbles. If a marble is drawn at random from the box, what is the probability that it will be
- white?
- blue?
- red?
If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = x^2- 3x - 2,$ find a quadratic polynomial whose zeroes are $\frac{1}{2\alpha+\beta}$ and $\frac{1}{2\beta+\alpha}.$
→