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.

Question

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.
OR

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth are 1.4 cm. Find the volume of wood in the entire stand.

Philoid · Accepted Answer

Radius of cylindrical and hemispherical part = 1.4 cm

Length of hemispherical part = 1.4 cm

Length of cylindrical part, h = 5 – (2 × 1.4) = 2.2 cm

Gulab jamun is shown below.

⇒ Volume of gulab jamun = volume of cylinder + 2 × volume of hemisphere

=

⇒ Volume of 45 gulab jamuns =

⇒ Syrup required = 30 % of above volume =

OR

Required volume = volume of cuboid – 4 × volume of cone

⇒ Required volume =

⇒

Hence, volume of wood in the entire sand is .