Question

3. A gulab jamun, contains sugar syrup up to about
30% of its volume. Find approximately how much
syrup would be found in 45 gulab jamuns, each
shaped like a cylinder with two hemispherical ends
with length 5 cm and diameter 2.8 cm (see Fig. 13.15).
Fig. 13.15
4. A pen stand made of wood is in the shape of a​

Answer 1

Given:

Volume :- 30%

Length:- 5cm

Diameter:- 2.8cm

To Find:

Volume of 45 gulab jamuns

Solution:

Diameter = 2.8 cm

So, radius of cylinder = radius of hemisphere, r =

$\dashrightarrow\: \sf\Large\ \frac{2.8}{2}$cm.

$\dashrightarrow\: \sf\ =1.4cm$

Length of gulab jamun = 5 cm

Height of cylinder, h = 5 - (1.4+1.4)

= 5 - 2.8

= 2.2 cm

Therefore, Volume of gulab jamun

= Volume of cylinder + 2 × Volume of Hemisphere

$\dashrightarrow\: \sf\ \pi {r}^{2} h + 2× \frac{2}{3} \pi {r}^{3}$

$\dashrightarrow\: \sf\ \pi {r}^{2} (h + \frac{4}{3} r)$

$\dashrightarrow\: \sf\ \frac{22}{7} \times 1.4 \times 1.4(2.2 + \frac{4}{3} \times 1.4)$

$\dashrightarrow\: \sf\ 22 \times 0.2 \times 1.4 \times \frac{6.6 + 5.6}{3}$

$\dashrightarrow\: \sf\ 6.16 \times \frac{12.2}{3}$

$\dashrightarrow\: \sf\ \frac{6.16 \times 12.2}{3}$

$\dashrightarrow\: \sf\ 6.16×12.= \frac{75.152}{3} \: cm^3$

Thus, Volume of 45 gulab jamuns,

$\dashrightarrow\: \sf\ = 45 \times \frac{75.152}{3}$

$\dashrightarrow\: \underline{\boxed{\bf{\orange{= 1127.28cm^3}}}}$

Answer 2

1127.28 cubic cm is your answer.

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