Surface Areas and Volumes

CLASS-X- Assignment

Q1) A solid cylinder has a total surface area 462 sq. cm. Its curved surface area is one third of the total surface area . Find the volume of the cylinder.

Q2) A cone of radius 10 cm is divided into 2 parts by drawing a plane through the mid point of its axis, parallel to its base. Compare the volume of the 2 parts.

Q3) A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume of :

a)-Water displaced out of the cylindrical vessel .

b)-Water left in the cylindrical vessel.

Q4) From a solid cylinder whose height is 8 cm and radius is 6cm, a conical cavity of height 8 cm and base radius 6cm, is hollowed out. Find the volume of the remaining solid correct to two places of decimals, also find the total surface area of the remaining solid. [Take – =3.14]

Q5) A sphere of diameter -12 cm is dropped in a right circular cylinder vessel partly filled with water. If the sphere is completely submerged in water the water level in the cylindrical vessel rises by 23/5 cm. Find the diameter of cylindrical vessel.

Q6) The vessel is in the form of open inverted cone of height 8 cm. Radius of its top is 5 cm. it is filled with water up to the brim. When some lead shots, each sphere of diameter 1 cm are dropped into the vessel, 1/8th of water flows out. Find out how many lead shots were dropped in the vessel.(HOTS) Q7) A spherical iron shell with 12 cm external diameter weighs 166320/21 gm. Find the thickness of the shell. If the density of the iron is 10 gm/cm.(HOTS)

Q8) The diameter of a roller 120 cm long is 84 cm. if it takes 500 complete revolution to level a playground. Determine the cost of leveling it at the rate of 30 paise per sq m.

Q9) The height of a cone is 60 cm. A small cone is cut off at the top by a plane parallel to the base and its volume is 1/64 of the volume of the original cone. Find the height from the base at which the section is made.(HOTS)

Q10) Find the volume of the largest right circular cone that can be cut off from a cube of edge 4.2 cm.

Q11) Find the volume of the largest right circular that can be cut off from a cube of edge of4.9 cm.

Q12) The slant height of a frustum of a cone is 5cm. If the difference between the two circular ends is 4cm. Write the height of frustum.

Q13) A cylinder, a cone and a hemisphere are of same base and of same height. Find the ratio of their volumes.

Q14) How many shots each having diameter 4.2cm can be made from a cuboidal lead solid of dimensions 66cm X 42cm X 21cm.

Q15) Find the number of metallic circular disks with 1.5cm base diameter and height of 0.2cm to be melted to form a metallic right circular cylinder of height 10cm and diameter of 4.5 cm.

Q16) From a solid cube of side 7cm, a conical cavity of side radius 3cm is hollowed out. Find the volume of the remaining solid.

Q17) A cubical block of side 7cm is surmounted by a hemisphere. What is the greatest diameter of the hemisphere can have ?Find the surface area of the solid. Q18) A spherical copper shell, of external diameter 16cm, is melted and recast into a solid cone of base radius 13cm and height 4cm. Find the inner diameter of the shell.(HOTS)

Q19) 21 glass spheres each of radius 2cm are packed in a cuboidal box of internal dimensions 16cm X 8cm X 8cm and then the box is filled with water. Find the volume of water filled in the box ?(HOTS)

Q20) A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains 313/21cm3 of air. If the internal diameter of the building is equal to its total height above the floor , Find the height of the building?(HOTS)

Q21) A shuttle cock used for playing badminton has the shape of frustum of cone mounted on a hemisphere. The external diameters of the frustum are 5cm and 2cm, the height of the entire shuttle cock is 7cm. Find the external surface area.