Q)  Adventure camps are the perfect place for the children to practice decision making for themselves without parents and teachers guiding their every move. Some students of a school reached for adventure at Sakleshpur. At the camp, the waiters served some students with a welcome drink in a cylindrical glass and some students in a hemispherical cup whose dimensions are shown below.

After that they went for a jungle trek. The jungle trek was enjoyable but tiring. As dusk fell, it was time to take shelter. Each group of four students was given a canvas of area 551m2 . Each group had to make a conical tent to accommodate all the four students. Assuming that all the stitching and wasting incurred while cutting, would amount to 1m2 , the students put the tents. The radius of the tent is 7m.

1. The volume of cylindrical cup is:

a) 295.75 cm^3.      b) 7415.5 cm³          c) 384.88 cm^3.           d) 404.25 cm³

2. The volume of hemispherical cup is:

a) 179.67 cm^3.       b) 89.83 cm³         c) 172.25 cm^3.        d) 210.60 cm³

3. Which container had more juice and by how much?

a) Hemispherical cup, 195 cm³                b) Cylindrical glass, 207 cm³

c) Hemispherical cup, 280.85 cm³         d) Cylindrical glass, 314.42 cm³

4. The height of the conical tent prepared to accommodate four students is

a) 18m     b) 10m      c) 24m    d) 14m

5. How much space on the ground is occupied by each student in the conical tent

a) 54 m²   b) 38.5 m²      c) 86 m²   d) 24 m²

Ans:

1. Cylindrical cup volume:

The volume of cylindrical cup is = π r ² h

= 7 cm, = cm

= 10.5 cm

Volume of cylindrical cup =

=

=

= 404.25 cm³

Hence, option d) is correct option.

2. Hemispherical cup volume:

The volume of hemispherical cup is =

= 7 cm, = cm

Volume of hemispherical cup =

=

=

=

= 89.83 cm³

Hence, option b) is correct option.

3. Larger container:

As we can see that the volume of cylindrical cup is more than the hemispherical cup, hence cylindrical cup will hold more juice.

Since the difference in the capacity = capacity of the cylindrical cup – capacity of the hemispherical  cup

= 404.25 – 89.83

= 314.42 cm³

Hence, option d) is correct option.

4. Height of the tent:

Given that the canvas area = 551 m²

Wastage of canvas = 1 m²

Net canvas used for making the tent = original area of canvas – wastage

= 551 – 1 = 550 m²

Since this canvas is used to make the conical tent,

The curved surface area of a conical tent is =

Given that the Radius of the conical tent, = 7 m

Now, from the adjoining figure: 

Here we have, = 7 m, = 25 m

= 625 – 49 = 576

= 24 m

Therefore, height of the conical tent is 24 m

Hence, option c) is correct option.

5. Ground space by each student in conical tent:

Ground space of the conical tent = area of the base of tent

The base area of a conical tent is : π r²

= 7 m

The base area of a conical tent =  

= 22 x 7 = 154 cm²

Since the tent can contain 4 students, hence the ground space will be equally shared by the 4 students.

Therefore, space covered by each student=

= 38.5 cm²

Hence, option b) is correct option. 

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