Case study (4 Marks)

Question 14 Marks

Read the following text carefully and answer the questions that follow:
A Ferris wheel $($or a big wheel in the United Kingdom$)$ is an amusement ride consisting of a rotating upright wheel with multiple passenger$-$carrying components $($commonly referred to as passenger cars, cabins, tubs, capsules, gondolas, or pods$)$ attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity.
After taking a ride in Ferris wheel, Aarti came out from the crowd and was observing her friends who were enjoying the ride . She was curious about the different angles and measures that the wheel will form. She forms the figure as given below.

$i.$ Find $\angle R O Q$.
$ii.$ Find $\angle RQP$.
$iii.$ Find $\angle RSQ$.
OR
Find $\angle ORP$.

Answer

$i$

$\angle ROQ +\angle RPQ =180^{\circ}$
$\angle ROQ +30^{\circ}=180^{\circ}$
$\angle ROQ =150^{\circ}$
$ii.$

$\angle RQP =\angle OQP -\angle OQR$
$=90^{\circ}-15^{\circ}$
$=75^{\circ}$
$iii.$

$\angle RSQ =\frac{1}{2} \angle ROQ$
$=\frac{1}{2} \times 150^{\circ}$
$\angle RSQ =75^{\circ}$
OR

$\angle ORP=90^{\circ}$
$\because$ radius and tangent are $\perp$ at point of contact

View full question & answer→

Question 24 Marks

Read the following text carefully and answer the questions that follow:
A teacher is a person whose professional activity involves planning, organizing, and conducting group activities to develop student's knowledge, skills, and attitudes as stipulated by educational programs. Teachers may work with students as a whole class, in small groups or one-to-one, inside or outside regular classrooms. In this indicator, teachers are compared by their average age and work experience measured in years.
For the same in 2015, the following distribution of ages (in years) of primary school teachers in a district was collected to evaluate the teacher on the above-mentioned criterion.

i. What is the total no of teachers?
ii. Find the class mark of class 15 - 20, 25 - 30 and 45 - 50?
iii. What is the no of teachers of age range 25 - 40 years?
OR
Which classes are having same no. of teachers?

Answer

i. No of teachers in the age-group $15-20$ years $=10$
No of teachers in the age-group $20-25$ years $=30$
No of teachers in the age-group 25-30 years $=50$
No of teachers in the age-group $30-35$ years $=50$
No of teachers in the age-group 35-40 years $=30$
No of teachers in the age-group 40-45 years $=5$
No of teachers in the age-group 45-50 years $=2$
Thus the total no of teachers
= 10 + 30 + 50 + 50 + 30 + 5 + 2
=177
ii. Class Mark of class $15-20=$
$=\frac{15+20}{2}=17.5$
Class Mark of class $25-30=$
$=\frac{25+30}{2}=27.5$
Class Mark of class $45-50=$
$=\frac{45+50}{2}=47.5$
iii. No of teachers in the age-group $25-30$ years $=50$
No of teachers in the age-group $30-35$ years $=50$
No of teachers in the age-group $35-40$ years $=30$
Thus the no of teachers in the age range 25 - 40 years
=50+50+30=130
OR
From the observation of the bar chart we find that :
No of teachers in the age-group 25-30 years $=50$
No of teachers in the age-group $30-35$ years $=50$
Thus the no of teacher in the class 25-30 and 30-35 is equal.

View full question & answer→

Question 34 Marks

Read the following text carefully and answer the questions that follow:
The front compound wall of a house is decorated by wooden spheres of diameter $21 \ cm,$ placed on small supports as shown in figure. $25$ such spheres are used for this purpose and are to be painted silver. Each support is a cylinder and is to be painted black.

$i.$ what will be the total surface area of the spheres all around the wall?
$ii$. Find the cost of orange paint required if this paint costs $20$ paise per $\ cm^2$.
$iii.$ How much orange paint in liters is required for painting the supports if the paint required is $3 ml$ per $\ cm^2$ ?
OR
What will be the volume of total spheres all around the wall?

Answer

$i.$ Diameter of a wooden sphere $=21 \ cm$.
therefore Radius of wooden sphere $( R )=\frac{21}{2} \ cm$
The surface area of $25$ wooden spares
$=25 \times 4 \pi R ^2$
$=25 \times 4 \times \frac{22}{7} \times\left(\frac{21}{2}\right)^2$
$=138,600 \ cm^2$
$ii$. Diameter of a wooden sphere $=21 \ cm$.
therefore Radius of wooden sphere $( R )=\frac{21}{2} \ cm$
The surface area of $25$ wooden spares
$=25 \times 4 \pi R ^2$
$=25 \times 4 \times \frac{22}{7} \times\left(\frac{21}{2}\right)^2$
$=138,600 \ cm^2$
The cost of orange paint $=20$ paise per $cm ^2$
Thus total cost
$=\frac{138600 \times 20}{100}= ₹ 27720$
$iii$. Radius of a wooden sphere $r=4 \ cm$.
Height of support $( h )=7 \ cm$
The surface area of $25$ supports
$=25 \times \pi r ^2 h$
$=25 \times \frac{22}{7} \times 4^2 \times 7$
$=8800 \ cm^2$
The cost of orange paint $=10$ paise per $cm ^2$
Thus total cost
$=0.1 \times 8800= ₹ 880$
OR
$ V =\frac{4}{3} \pi r ^3 \times 25$
$V=25 \times \frac{4}{3} \times \frac{22}{7} \times\left(\frac{21}{6}\right)^?$
$25 \times \frac{4}{3} \times \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2} \times \frac{21}{2}$
$=25 \times 11 \times 21 \times 21$
$=121275 \ cm^3$

View full question & answer→

Maths Case study (4 Marks)

Test yourself on this topic