Volume and Surface Area Questions

• Two circles are having radii 9 cm and 12 cm. The distance between their centres is 15 cm. What is the length (in cm) of their common chord?
• Two circles touch each other at point X. Two common tangents of the circles meet at point P and none of the tangents passes through X. These tangents touch the larger circle at points B and C. If the radius of the larger circle is 15 cm and CP = 20 cm, then what is the radius (in cm) of the smaller circle?
• There are 8 equidistant points A, B, C, D, E, F, G and H (in same order) on a circle. What is the value of ∠FDH (in degrees)?
• An equilateral triangle of area 300 cm2 is cut from its three vertices to form a regular hexagon. Area of hexagon is what percent of the area of triangle?
• The sum of radii of the two circles is 91 cm and the difference between their area is 2002 cm2 . What is the radius (in cm) of the larger circle?
• The height of a cone is 45 cm. It is cut at a height of 15 cm from its base by a plane parallel to its base. If the volume of the smaller cone is 18480 cm3, then what is the volume (in cm3) of the original cone?
• Identical cubes of largest possible size are cut from a solid cuboid of size 65 cm × 26 cm × 3.9 cm. What is the total surface area (in cm2) of all the small cubes taken together?
• A regular triangular pyramid is cut by 2 planes which are parallel to its base. The planes trisects the altitude of the pyramid. Volume of top, middle and bottom part is V1, V2 and V3 respectively. What is the value of V1 :V2 : V3?
• The length, breadth and height of a cuboid are 12 cm, 8 cm and 6 cm respectively. The volume of the cuboid is (Use π = 22/7)
• A regular hexagonal base prism has height 8 cm and side of base is 4 cm. What is the total surface area (in cm2) of the prism?
• A cylinder of radius 4.5 cm and height 12 cm just fits in another cylinder completely with their axis perpendicular. What is the radius (in cm) of second cylinder?
• Two spheres of equal radius are taken out by cutting from a solid cube of side (12 + 4√3) cm. What is the maximum volume (in cm3) of each sphere?
• Three toys are in a shape of cylinder, hemisphere and cone. The three toys have same base. Height of each toy is 2√2 cm. What is the ratio of the total surface areas of cylinder, hemisphere and cone respectively?
• A solid cube is cut into 27 identical cubes. What is the percentage increase in the total surface area?
• A regular square pyramid has side of its base 20 cm and height 45 cm is melted and recast into regular triangular pyramids of equilateral base of side 10 cm and height 10√3 cm. What are the total numbers of regular triangular pyramid?
• If a cylinder of radius 7 cm and height 9 cm is melted and constructed into a cone of the same radius, what will be the height of this cone?
• What is the measure of an interior angle of a regular dodecagon?
• Find the curved surface area (in cm2) of a right circular cylinder of diameter 28 cm and height 12 cm.
• A cone of height 12 cm and diameter 10 cm is mounted on a hemisphere of the same diameter. What is the volume of the solid thus formed?
• At least two pairs of consecutive angles are congruent in a _____.