<p> Surface Areas and Volumes </p><p>CLASS-X- Assignment </p><p>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.</p><p>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.</p><p>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 :</p><p> a)-Water displaced out of the cylindrical vessel .</p><p> b)-Water left in the cylindrical vessel.</p><p>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]</p><p>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.</p><p>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)</p><p>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.</p><p>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)</p><p>Q10) Find the volume of the largest right circular cone that can be cut off from a cube of edge 4.2 cm.</p><p>Q11) Find the volume of the largest right circular that can be cut off from a cube of edge of4.9 cm.</p><p>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.</p><p>Q13) A cylinder, a cone and a hemisphere are of same base and of same height. Find the ratio of their volumes.</p><p>Q14) How many shots each having diameter 4.2cm can be made from a cuboidal lead solid of dimensions 66cm X 42cm X 21cm.</p><p>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.</p><p>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.</p><p>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)</p><p>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)</p><p>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)</p><p>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.</p>