**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 551 m ^{2} . 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 1 m^{2} , 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 cm^{3 }c) 384.88 cm^{3 }d) 404.25 cm^{3}**

**2. The volume of hemispherical cup is:**

**a) 179.67 cm ^{3 }b) 89.83 cm^{3 }c) 172.25 cm^{3 }d) 210.60 cm^{3}**

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

**a) Hemispherical cup, 195 cm ^{3 }b) Cylindrical glass, 207 cm^{3}**

**c) Hemispherical cup, 280.85 cm ^{3 }d) Cylindrical glass, 314.42 cm^{3}**

**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 m ^{2} b) 38.5 m^{2} c) 86 m^{2} d) 24 m^{2}**

**Ans:**

**1. Cylindrical cup volume:**

The volume of the cylindrical cup is = π r ^{2 }h

Given: D_{cyl} = 7 cm, ∴ R_{cyl} = cm; and H_{cyl} = 10.5 cm

∴ The volume of the cylindrical cup =

= x (10.5)

= 11 x x 10.5

= 404.25 cm^{3}

**Hence, option d) is the correct option.**

**2. Hemispherical cup volume:**

The volume of hemispherical cup is =

Given: D_{hemi }= 7 cm, ∴ R_{hem} = cm

∴ The volume of the hemispherical cup =

=

=

=

=

= 89.83 cm^{3}

**Hence, option b) is the 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 cm ^{3}**

**Therefore, the Cylindrical cup will hold 314.42 cm ^{3} more juice.**

**Hence, option d) is the correct option.**

**4. Height of the tent:**

Given: the area of the canvas = 551 m^{2}

Wastage of canvas = 1 m^{2}

∴ The net canvas used for making the conical tent = original area of canvas – wastage

= 551 – 1 = 550 m^{2}

Now this net canvas is used to make a tent,

Next, the Curved Surface Area of a conical tent is = π r l

Given: the radius of the conical tent, R_{con} = 7 m

∴ 550 = π x 7 x L_{con}

∴ 550 = x 7 x L_{con}

∴ 550 = 22 x L_{con}

∴ L_{con} = = 25 m

Now, from the adjoining figure:

(H_{con}) ^{2} + (R_{con}) ^{2} = (L_{con}) ^{2}

∴ (H_{con})^{2} = (L_{con})^{2} – (R_{con})^{2}

Now, we already have, R_{con} = 7 m, L_{con }= 25 m

∴ (H_{con})^{2} = (25) ^{2} – (7) ^{2} = 625 – 49 = 576

∴ H_{con }= √ 576 = 24 m

Therefore, the height of the conical tent is 24 m

**Hence, option c) is the correct option.**

**5. Ground space by each student in a conical tent:**

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

∵ The base area of a conical tent = π r ^{2}

and R_{con} = 7 m

The base area of a conical tent = π r ^{2 } = x (7)^{2 }

= 22 x 7 = 154 cm^{2}

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 cm^{2}

**Hence, option b) is the correct option. **

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