Mathematics · Textbook solutions

Surface Area and Volume

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 34 questions

Practice Set 9.1

8 q
  1. Ex 9.1 Q1
    Length, breadth and height of a cuboid shape box of medicine is 20 cm, 12 cm and 10 cm respectively. Find the surface area of vertical faces and total surface area of this box.
  2. Ex 9.1 Q2
    Total surface area of a box of cuboid shape is 500 sq. unit. Its breadth and height is 6 unit and 5 unit respectively. What is the length of that box ?
  3. Ex 9.1 Q3
    Side of a cube is 4.5 cm. Find the surface area of all vertical faces and total surface area of the cube.
  4. Ex 9.1 Q4
    Total surface area of a cube is 5400 sq. cm. Find the surface area of all vertical faces of the cube.
  5. Ex 9.1 Q5
    Volume of a cuboid is 34.50 cubic metre. Breadth and height of the cuboid is 1.5 m and 1.15 m respectively. Find its length.
  6. Ex 9.1 Q6
    What will be the volume of a cube having length of edge 7.5 cm ?
  7. Ex 9.1 Q7
    Radius of base of a cylinder is 20 cm and its height is 13 cm, find its curved surface area and total surface area. (π=3.14)(\pi = 3.14)
  8. Ex 9.1 Q8
    Curved surface area of a cylinder is 1980 cm2^2 and radius of its base is 15 cm. Find the height of the cylinder. (π=227)(\pi = \dfrac{22}{7})

Practice Set 9.2

10 q
  1. Ex 9.2 Q1
    Perpendicular height of a cone is 12 cm and its slant height is 13 cm. Find the radius of the base of the cone.
  2. Ex 9.2 Q2
    Find the volume of a cone, if its total surface area is 7128 sq.cm and radius of base is 28 cm. (π=227)(\pi = \dfrac{22}{7})
  3. Ex 9.2 Q3
    Curved surface area of a cone is 251.2 cm2^2 and radius of its base is 8 cm. Find its slant height and perpendicular height. (π=3.14)(\pi = 3.14)
  4. Ex 9.2 Q4
    What will be the cost of making a closed cone of tin sheet having radius of base 6 m and slant height 8 m if the rate of making is Rs. 10 per sq.m ?
  5. Ex 9.2 Q5
    Volume of a cone is 6280 cubic cm and base radius of the cone is 30 cm. Find its perpendicular height. (π=3.14)(\pi = 3.14)
  6. Ex 9.2 Q6
    Surface area of a cone is 188.4 sq.cm and its slant height is 10 cm. Find its perpendicular height. (π=3.14)(\pi = 3.14)
  7. Ex 9.2 Q7
    Volume of a cone is 1212 cm3^3 and its height is 24 cm. Find the surface area of the cone. (π=227)(\pi = \dfrac{22}{7})
  8. Ex 9.2 Q8
    The curved surface area of a cone is 2200 sq.cm and its slant height is 50 cm. Find the total surface area of cone. (π=227)(\pi = \dfrac{22}{7})
  9. Ex 9.2 Q9
    There are 25 persons in a tent which is conical in shape. Every person needs an area of 4 sq.m. of the ground inside the tent. If height of the tent is 18 m, find the volume of the tent.
  10. Ex 9.2 Q10
    In a field, dry fodder for the cattle is heaped in a conical shape. The height of the cone is 2.1 m and diameter of base is 7.2 m. Find the volume of the fodder. If it is to be covered by polythene in rainy season then how much minimum polythene sheet is needed ? (π=227(\pi = \dfrac{22}{7} and 17.37=4.17)\sqrt{17.37} = 4.17)

Practice Set 9.3

7 q
  1. Find the surface areas and volumes of spheres of the following radii. (π=3.14)(\pi = 3.14)
    Ex 9.3 Q1(i)
    4 cm
  2. Ex 9.3 Q1(ii)
    9 cm
  3. Ex 9.3 Q1(iii)
    3.5 cm
  4. Ex 9.3 Q2
    If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. (π=3.14)(\pi = 3.14)
  5. Ex 9.3 Q3
    If the surface area of a sphere is 2826 cm2^2 then find its volume. (π=3.14)(\pi = 3.14)
  6. Ex 9.3 Q4
    Find the surface area of a sphere, if its volume is 38808 cubic cm. (π=227)(\pi = \dfrac{22}{7})
  7. Ex 9.3 Q5
    Volume of a hemisphere is 18000 π18000\,\pi cubic cm. Find its diameter.

Problem Set 9

9 q
  1. Prob Q1
    If diameter of a road roller is 0.9 m and its length is 1.4 m, how much area of a field will be pressed in its 500 rotations ?
  2. Prob Q2
    To make an open fish tank, a glass sheet of 2 mm gauge is used. The outer length, breadth and height of the tank are 60.4 cm, 40.4 cm and 40.2 cm respectively. How much maximum volume of water will be contained in it ?
  3. Prob Q3
    If the ratio of radius of base and height of a cone is 5 : 12 and its volume is 314 cubic metre, find its perpendicular height and slant height. (π=3.14)(\pi = 3.14)
  4. Prob Q4
    Find the radius of a sphere if its volume is 904.32 cubic cm. (π=3.14)(\pi = 3.14)
  5. Prob Q5
    Total surface area of a cube is 864 sq.cm. Find its volume.
  6. Prob Q6
    Find the volume of a sphere, if its surface area is 154 sq.cm.
  7. Prob Q7
    Total surface area of a cone is 616 sq.cm. If the slant height of the cone is three times the radius of its base, find its slant height.
  8. Prob Q8
    The inner diameter of a well is 4.20 metre and its depth is 10 metre. Find the inner surface area of the well. Find the cost of plastering it from inside at the rate Rs. 52 per sq.m.
  9. Prob Q9
    The length of a road roller is 2.1 m and its diameter is 1.4 m. For levelling a ground 500 rotations of the road roller were required. How much area of ground was levelled by the road roller ? Find the cost of levelling at the rate of Rs. 7 per sq. m.