MEDIUM
10th Assam Board
IMPORTANT
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A gulabjamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulabjamuns, each shaped like a cylinder with two hemispherical ends with length 5cm and diameter 2.8cm (see Fig.).

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Important Questions on Surface Areas and Volumes

MEDIUM
10th Assam Board
IMPORTANT

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 is 1.4 cm. Find the volume of wood in the entire stand (see figure).

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HARD
10th Assam Board
IMPORTANT
A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
MEDIUM
10th Assam Board
IMPORTANT
A solid iron pole consists of a cylinder of height 220cm and base diameter 24cm, which is surmounted by another cylinder of height 60cm and radius 8cm. Find the mass of the pole, given that 1cm3 of iron has approximately 8g mass. (Use π=3.14)
MEDIUM
10th Assam Board
IMPORTANT
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
MEDIUM
10th Assam Board
IMPORTANT
A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm3. Check whether she is correct, taking the above as the inside measurements, and π=3.14.
MEDIUM
10th Assam Board
IMPORTANT
A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.
MEDIUM
10th Assam Board
IMPORTANT
Metallic spheres of radii 6 cm,8 cm and 10 cm respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.
MEDIUM
10th Assam Board
IMPORTANT
A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform.