Case study (4 Marks)

Question 14 Marks

Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health-conscious individuals.

500 mL milk is packed in a cuboidal container of dimensions $15 cm \times 8 cm \times 5 cm$. These milk packets are then packed in cuboidal cartons of dimensions $30 cm \times 32 cm \times 15 cm$.
Based on the above given information, answer the following questions:
(i) Find the volume of the cuboidal carton.
(ii) (a) Find the total surface area of a milk packet.
OR
(b) How many milk packets can be filled in a carton?
(iii) How much milk can the cup (as shown in the figure) hold?

Answer

$
\text { (i) } \begin{aligned}
\text { Volume of cuboidal carton } & =30 \times 32 \times 15 \\
& =14400 cm^3
\end{aligned}
$
(ii)(a) Total surface area of milk packet $=2(15 \times 8+8 \times 5+5 \times 15)$
$
=470 cm^2
$
OR
(ii) $
\text { (b) } \begin{aligned}
\text { Number of milk packets in carton } & =\frac{30 \times 32 \times 15}{15 \times 8 \times 5} \\
& =24
\end{aligned}
$
(iii) Capacity of the $\operatorname{cup}=\frac{22}{7} \times 5 \times 5 \times 7$
$
=550 cm^3 \text { or } 550 ml
$

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Question 24 Marks

Treasure Hunt is an exciting and adventurous game where participants follow a series of clues/numbers/maps to discover hidden treasures. Players engage in a thrilling quest, solving puzzles and riddles to unveil the location of the coveted prize.
While playing a treasure hunt game, some clues (numbers) are hidden in various spots collectively forming an $A.P$. If the number on the $n^{\text {th }}$ spot is $20+4 n$, then answer the following questions to help the players in spotting the clues:

$(i)$ Which number is on first spot?
(ii) (a) Which spot is numbered as $112$?
$\text{OR}$
$(b)$ What is the sum of all the numbers on the first $10$ spots?
$(iii)$ Which number is on the $( n -2)^{ th }$ spot?

Answer

$(i)$ Number on the first spot $=20+4 \times 1=24$
$(ii) (a)$
$20+4 n=112$
$\Rightarrow n=23$
$\text{OR}$
$(ii) (b)$
$d =4$
$S_{10} =\frac{10}{2}[2 \times 24+9 \times 4]$
$ =420$
$(iii)$
Number on the $(n-2)^{th}$ spot $=20+4(n-2)$
$ =12+4 n$

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Question 34 Marks

Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So he started to sketch his own rocket designs on the graph sheet. One such design is given below :

Based on the above, answer the following questions:
(i) Find the mid-point of the segment joining F and G .
(ii) (a) What is the distance between the points A and C ?
OR
(b) Find the coordinates of the point which divides the line segment joining the points A and B in the ratio $1: 3$ internally.
(iii) What are the coordinates of the point D ?

Answer

(i) Mid point of FG is $\left(\frac{-3+1}{2}, \frac{0+4}{2}\right)=(-1,2)$
(ii) (a)
$
\begin{aligned}
AC & =\sqrt{(-1-3)^2+(-2-4)^2} \\
& =\sqrt{52} \text { or } 2 \sqrt{13}
\end{aligned}
$
OR
(ii) (b) The coordinates of required point are $\left(\frac{1 \times 3+3 \times 3}{1+3}, \frac{1 \times 2+3 \times 4}{1+3}\right)$
i.e. $\left(3, \frac{7}{2}\right)$
(iii) $D (-2,-5)$

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Maths Case study (4 Marks)

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