page1 Class 9 maths 13. Surface Areas and Volumes - CBSE Notes - Toppers Study

Additional -Questions With Solutions

Q1. A cube and cuboid have same volume. The dimenstions of the cuboid are in the ratio 1 : 2: 4. if the difference between the cost of polishing the cube and cuboid at the rate of Rs. 5 per m² is 80, find their volumes. 

Ans: 64 m³

Q2. The sum of length, breadth and depth of a cuboid is 19 cm and  the length of the diagonal in 11 cm. Find the surface area of the cuboid. 

                                   Ans: 240 cm²

Q3. The ratio of the curved surface area to the total surface area of a right circular cylinder is 1: 3. Find the volume of the cylinder if its total surface area is 1848 cm². 

Ans: 4312 cm³

Q4. The cost of papering four walls of a room at Rs. 1.50 per square meter is Rs. 337.50. The height of the room is 5 m. Find the length and breadth of the room if they are in the ratio 4 : 1. 

Ans: l = 18 m, b= 4.5 

Q5. Circumference of the base of a cylinder open at top is 132 cm. The sum of radius and height of the cylinder 41 cm. FInd the cost of polishing the outer surface of cylinder at rate of Rs. 10 per square metre. 

Ans: Rs. 4.026 

Q6. The total surface area of a right circular cylinder is 6512 cm², and the circumference of its base is 88 cm, find the volume of the cylinder. 

Ans: 36960 cm³ 

Q7. The areas of three adjacent faces of a cuboid are 108 cm², 72 cm² and 96 cm² respectively. Find the volume of the cuboid. Also find the dimensions of the cuboid. 

 Ans: Volume = 864 cm², dimensions 12 cm x 9 cm x 8 cm 

Q8. A right circular cone is 5.4 cm high and radius of its base is 2 cm. It is melted and recast into another right circular cone with radius of base as 1.5 cm. Find the height of the new cone formed. 

Ans: 9.6 cm 

Q9. The radius  and height of a right circular cone are in the ratio 3 : 4. If its volume is 301.44 cm³, find its radius and slaint height. [take  π = 3.14]

Ans: Radius : 6 cm, height = 10 cm 

Q10. Four cubes each of side 5 cm are joined end to end. Find surface area of resultant cuboid. 

Ans: 450 cm²

Q11. A hemispherical dome of a building needs to be painted. If the circumference of the base of dome is 17.6 m, find the cost of painting it, at the rate of 5 per 100 cm². 

Ans: Rs. 24640

Q12.  The difference between outsite and inside surfaces of cylinderical metallic pipe 14 cm ling is 44 cm². If a pipe is made of 99 cm³ of metal, find the outer and inner radii of the pipe. 

Ans: R = 2.5 cm, r = 2 cm 

Q13. If in a sphere, volume  and surface area are numerically equal, find the radius. 

Ans: r = 3 units

Q14. Rain water which falls on a flat rectangular surface of length 6 m and breadth 4 m is transferred into a cylindrical vessel of internal radius 20 cm. What will be height of water in the cylinderical vessel if the rainfall is 1 cm ? Give naswer to the nearest whole number. [use  π = 3.14]

Ans: 192 cm

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