Surface Areas and Volumes
23 solved questions from Class 10 Mathematics, each with the full working. Tap any question to see the step-by-step solution.
- 1 A solid sphere and a solid right circular cylinder have the same total surface area. If the radius of the sphere is 7 cm, find the height of the cylinder. (Take π = 22/7.) medium 4 marks Equality of sphere and cylinder surface areas
- 2 A solid cone is formed by rotating a right triangle having base 12 cm and height 9 cm about its height. Find the volume of the cone. Give your answer in cubic centimeters, correct to the nearest cm^3. medium 3 marks Volume of a cone
- 3 Find the total surface area of a cube whose each edge measures 5 cm. easy 1 mark Surface area of a cube
- 4 The curved surface area of a right circular cone is 150π cm^2. If its slant height is 15 cm, find the radius of its base. medium MCQ 2 marks Curved surface area of a cone
- 5 A solid right circular cylinder has radius 5 cm and height 12 cm. Find its total surface area. Use π = 22/7 and give the answer in square centimetres, correct to the nearest integer. medium 2 marks Total surface area of a cylinder
- 6 Find the total surface area of a solid sphere of radius 5 cm. Take π=22/7 and give the answer to the nearest square centimetre. easy 2 marks Surface area of sphere
- 7 Solve the expression: 15 + 25 × 2. medium MCQ BODMAS Rule
- 8 Find the area of a rectangle with length 8 cm and breadth 5 cm. medium MCQ Area of Rectangle
- 9 What is the volume of a cube with edge 3 cm? medium MCQ Volume of Cube
- 10 Find the 10th term of AP: 2, 7, 12, ... medium MCQ Arithmetic Progression
- 11 Distance between points (0,0) and (6,8) is: medium MCQ Distance Formula
- 12 Find surface area of a sphere with radius 7 cm (π = 22/7). medium MCQ Surface Area of Sphere
- 13 If perimeter of a circle is equal to that of a square, find ratio of their areas. medium MCQ Areas Related to Circles
- 14 What is the nth term of an AP with first term a and common difference d? medium MCQ Arithmetic Progression
- 15 Coordinates of midpoint of line joining (x₁, y₁) and (x₂, y₂) is: medium MCQ Midpoint Formula
- 16 Find the value of (2⁰ + 3⁰) × 5⁰. medium MCQ Exponent Laws
- 17 What is the domain, range, or fundamental theorem introduced in 'Surface Areas and Volumes' (Class 10 Mathematics)? medium MCQ Functions & Theorems
- 18 What is the derivative or integral formula associated with 'Surface Areas and Volumes'? medium MCQ Calculus & Formulae
- 19 How do you find the solution set or optimum value in 'Surface Areas and Volumes'? medium MCQ Problem Solving & Optimization
- 20 A solid right circular cylinder and a solid sphere have the same total surface area. The cylinder has radius 5 cm and unknown height. The sphere has radius 7 cm. Find the height of the cylinder. Take π=22/7 and give the answer to one decimal place. medium 3 marks Equality of cylinder and sphere surface areas
- 21 A right triangle has base 9 cm and height 12 cm. When it is rotated about its height, it forms a solid. What is the volume of the solid? Take π=22/7. Choose the correct option. hard MCQ 4 marks Volume of cone by rotation
- 22 Calculate the total surface area of a right circular cylinder with radius 4,cm and height 9,cm (use π=22/7). Give the answer to the nearest square centimetre. medium 2 marks Cylinder surface area
- 23 A right triangle has a base of 9,cm and a height of 12,cm. When the triangle is rotated about its base, it forms a right circular cone. What is the volume of the resulting solid? (Take π=22/7). hard MCQ 3 marks Cone volume by rotation