Case study (4 Marks)

Question 14 Marks

In a survey on holidays, 120 people were asked to state which type of transport they used on their last holiday. The following pie chart shows the results of the survey.

Observe the pie chart and answer the following questions:
(i) If one person is selected at random, find the probability that he/she travelled by bus or ship.
(ii) Which is most favourite mode of transport and how many people used it?
(iii) (a) A person is selected at random. If the probability that he did not use train is $4 / 5$, find the number of people who used train.
OR
(iii) (b) The probability that randomly selected person used aeroplane is 7/60. Find the revenue collected by air company at the rate of ₹ 5,000 per person.

Answer

(i) P (travelling by bus or ship) $=\frac{36+33}{360}=\frac{69}{360}$ or $\frac{23}{120}$
(ii) Car Number of people who used car $=\frac{177}{360} \times 120=59$
(iii) (a) $P$ (person used train) $=1-\frac{4}{5}=\frac{1}{5}$
$\therefore$ Number of people who used train $=\frac{120}{5}=24$
OR
(iii) (b) Number of people who used aeroplane $=\frac{7}{60} \times 120=14$
$\therefore$ Revenue generated $=14 \times 5000=$ ₹70,000

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Question 24 Marks

The word 'circus' has the same root as 'circle'. In a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd.
A circus tent is cylindrical upto a height of $8 m$ and conical above it. The diameter of the base is $28 m$ and total height of tent is $18.5 m .$

Based on the above, answer the following questions :
$(i)$ Find slant height of the conical part.
$(ii)$ Determine the floor area of the tent.
$(iii) (a)$ Find area of the cloth used for making tent.
OR
$(iii) (b) $Find total volume of air inside an empty tent.

Answer

$(i)$ Height of conical part $=18.5-8=10.5 m$
Radius of conical part $=14 m$
Slant height $=\sqrt{(10.5)^2+(14)^2}=17.5 m$
$(ii)$ Floor area $=\frac{22}{7} \times 14 \times 14=616 m^2$
$(iii) (a)$ Area of cloth used
$=2 \times \frac{22}{7} \times 14 \times 8+\frac{22}{7} \times 14 \times 17.5$
$=1474 m^2$
$\text{OR}$
$(iii) (b)$ Volume of air inside the tent
$=\frac{22}{7} \times 14 \times 14 \times 8+\frac{1}{3} \times \frac{22}{7} \times 14 \times 14 \times 10.5$
$=7084 m^3$

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Question 34 Marks

A ball is thrown in the air so that $t$ seconds after it is thrown, its height $h$ metre above its starting point is given by the polynomial $h=25 t-5 t^2$.

Observe the graph of the polynomial and answer the following questions:
$(i)$ Write zeroes of the given polynomial.
$(ii)$ Find the maximum height achieved by ball.
$(iii) (a)$ After throwing upward, how much time did the ball take to reach to the height of $30 m ?$
$\text{OR}$
$(iii) (b)$ Find the two different values of $t$ when the height of the ball was $20 m.$

Answer

$(i)$ Zeroes of the polynomial are $0$ and $5$
$(ii)$ Maximum height achieved by ball
$=25 \times \frac{5}{2}-5 \times\left(\frac{5}{2}\right)^2$
$=\frac{125}{4}$ or $31.25 m$
$\text { (iii)(a) }-5 t^2+25 t=30$
$\Rightarrow t^2-5 t+6=0$
$\Rightarrow(t-2)(t-3)=0$
$ t \neq 3, t=2$
$\text{OR}$
$\text {(iii)(b) }-5 t^2+25 t=20$
$\Rightarrow t^2-5 t+4=0$
$\Rightarrow(t-4)(t-1)=0$
$\Rightarrow t=4,1$

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Maths Case study (4 Marks)

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