CBSE Class 10 Surface Areas and Volumes Sure Shot Questions Set I

Question. A sphere of diameter 6 cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel ?
Answer: 1 cm

Question. The largest sphere is carved out of a cube of side 7 cm. Find the volume of the sphere.
Answer: \( 179 \frac{2}{3} \text{ cm}^3 \)

Question. A vessel, in the form of a hemispherical bowl, is full of water. Its contents are emptied in a right circular cylindrical. The internal radii of the bowl and the cylinder are 3.5 cm and 7 cm respectively. Find the height to which water will rise in the cylinder.
Answer: \( \frac{7}{12} \text{ cm} \)

Question. An iron pillar has some part in the form of a right circular cylindrical and the remaining in the form of a right circular cone. The radius of the base of each of the cone and cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the weight of the pillar if one cu cm of iron weights 7.8 grams.
Answer: 395.37 kg.

Question. A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy.
Answer: \( 266.112 \text{ cm}^3 \)

Question. A hemispherical bowl of internal diameter 36 cm contains a liquid. This liquid is to be filled in cylindrical bottles of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl?
Answer: 72

Question. Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm, containing some water. Find the number of marbles that should be dropped into the beaker so that the level rises by 5.6 cm.
Answer: 150

Question. The curved surface area of the right circular cone is \( 12320 \text{ cm}^2 \). If the radius of the base is 56 cm, find its height.
Answer: 42 cm

Question. The circumference of the edge of a hemispherical bowl is 12 cm. Find the capacity of the bowl.
Answer: \( 19404 \text{ cm}^3 \)

Question. The volume of a vessel in the form of a right circular cylindrical is \( 448\pi \text{ cm}^3 \) and its height is 7 cm. Find the radius of its base.
Answer: 8 cm

Question. A building is in the form of a cylinder surmounted by a hemispherical walled dome and contains \( 41 \frac{19}{21} \text{ m}^3 \) of air. If the internal diameter of the building is equal to its total height above the floor, find the height of the building.
Answer: 4 m

Question. The volume of a right circular cylinder of height 7 cm is \( 567\pi \text{ cm}^3 \). Find its curved surface area.
Answer: \( 393 \text{ cm}^2 \)

Question. If the radius of the base of a right circular cylinder is halved, keeping the height same, find the ratio of the volume of the reduced to that of the original cylinder.
Answer: 1 : 4

Question. Two right circular cones X and Y are made, X having three times the radius of Y and Y having half the volume of X. Calculate the ratio of heights of X and Y.
Answer: 2 : 9

Question. How many metres of cloth 5m wide will be required to make a conical tent, the radius of whose base is 7m and whose height is 24 cm.
Answer: 110 m

Question. The radii of the internal and external surface of a hollow spherical shell are 3 cm and 5 cm respectively. If it is melted and recast into a solid cylinder of height \( 2 \frac{2}{3} \text{ cm} \), find the diameter and the curved surface area of the cylinder.
Answer: 14 cm, \( \frac{352}{3} \text{ cm}^2 \)

Question. A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm. Find the total surface area and the volume of the toy.
Answer: \( 214.5 \text{ cm}^2, 243.83 \text{ cm}^3 \)

Question. The radii of the ends of the frustum of a right circular cone are 5 metres and 8 metres and its lateral height is 5m Find the lateral surface area and the volume of the frustum. Take \( \pi = 3.142 \).
Answer: \( 204.23 \text{ m}^2, 540.42 \text{ m}^3 \)

Question. A hemispherical bowl of internal diameter 30 cm is full of some liquid. This liquid is to be filled into cylindrical shaped bottles each of diameter 5 cm and height 6 cm. Find the number of bottle necessary to empty the bowl.
Answer: 60

Question. If the radii of the circular ends of a bucket, 45 cm high, are 28 cm and 7 cm, find the capacity and the total surface area of the bucket.
Answer: \( 48510 \text{ cm}^3, 5616.6 \text{ cm}^2 \)

Question. A hollow cone is cut by a plane parallel to the base and upper portion is removed. If the curved surface area of the remainder is \( \frac{8}{9} \) of the curved surface area of the whole cone, find the ratio of the line segments into which the altitude of the cone is divided by the plane.
Answer: 1 : 2

Question. The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area.
Answer: \( 7599.43 \text{ cm}^2 \)

Question. The rain water from a roof 22 m \( \times \) 20 m drains into a cylindrical vessel having diameter of base 2m and height 3.5m. If the vessel is just full, find the rainfall in cm.
Answer: 2.5 cm

Question. A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the bucket if the cost of the metal sheet used is -j 15 per 100 \( \text{cm}^2 \). (Use \( \pi = 3.14 \))
Answer: -j 293.90

Question. Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Find the time in which the level of water in the tank will rise by 21 cm.
Answer: 2 hr.

Question. A bucket made up of a metal sheet is in the form of a frustum of a cone. Its depth is 24 cm and the diameters of the top and the bottom are 30 cm and 10 cm respectively. Find the cost of milk which can completely fill the bucket at the rate of -j . 20 per litre and the cost of the metal sheet used, if it costs -j 10 per 100 \( \text{cm}^2 \). (Use \( \pi = 3.14 \)).
Answer: -j 163 approx, -j 171 approx

Question. A bucket is in the form of a frustum of a cone with a capacity of \( 12308.8 \text{ cm}^3 \) of water. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of the metal used in making it (Use \( \pi = 3.14 \)).
Answer: 15 cm, \( 2160.32 \text{ cm}^2 \)

Question. A sphere of diameter 12 cm, is dropped into a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, The water level in the cylindrical vessel rises by \( 3 \frac{5}{9} \text{ cm} \). Find the diameter of the cylindrical vessel.
Answer: 9 cm

Question. Find the number of coins 1.5 cm in diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
Answer: 450

Question. Water flows out through a circular pipe whose internal radius is 1 cm, at the rate of 80 cm / sec into an empty cylindrical tank, the radius of whose base is 40 cm. By how much will the level of water rise in the tank in half an hour ?
Answer: 90 cm

Question. The adjoining figure shows the cross–section of an ice–cream cone consisting of a cone surmounted by a hemisphere. The radius of the hemisphere is 3.5 cm and the height of the cone is 10.5 cm. The outer shell ABCDEF is shaded and is not filled with ice cream. AE = DC = 0.5 cm, AB || EF and BC || FD. Calculate (i) The volume of the ice-cream in the cone (the unshaded portion including the hemisphere) in \( \text{cm}^3 \); (ii) The volume of the outer shell (the shaded portion) in \( \text{cm}^3 \). Give your answer correct to the nearest \( \text{cm}^3 \).
Answer: (i) \( 175 \text{ cm}^3 \) (ii) \( 50 \text{ cm}^3 \)

Question. (a) The figure (i) given below, shows a cuboidal block of wood through which a circular cylindrical hole of the biggest size is drilled. Find the volume of the wood left in the block. (b) The figure (ii) given below, shows a solid trophy made of shinning glass. If one cubic centimeter of glass costs -j 0.75, find the cost of the glass for making the trophy.
Answer: (a) \( 13500 \text{ cm}^3 \) (b) -j 29400.