      Q) From a solid right circular cylinder of height 14 cm and base radius 6 cm, a right circular cone of same height and same base radius is removed. Find the volume of the remaining solid. Ans: Step 1: ∵ Volume of the cylinder = π r 2 h For cylinder, […]
surface areas and volumes
      Q) A metallic cylinder has radius 3 cm and height 5 cm. To reduce its weights, a conical hole is drilled in the cylinder. The conical hole has a radius of cm and its depth cm. Calculate the ratio of the volume of metal left in the cylinder to the
Q) A chord of a circle of radius 15 cm subtends an angle of 60° at the centre of the circle. Find the area of the corresponding minor segment. (π = 3.14, √3 = 1.73). UP Board 2024 (822 HY) Ans: For a detailed answer to this question, please refer to the similar question and
      Q) In the diagram given below, a tilted right circular cylindrical vessel with base diameter 7 cm contains a liquid. When placed vertically, the height of the liquid in the vessel is the mean of two heights shown in the diagram. Find the area of wet surface, when the cylinder
Q) A manufacturing company prepares spherical ball bearings, each of radius 7 mm and mass 4 gm. These ball bearings are packed into boxes. Each box can have a maximum of 2156 cm³ of ball bearings. Find the:(a) maximum number of ball bearings that each box can have.(b) mass of each box of ball bearings
Q) From a solid right circular cone, whose height is 6 cm and radius of base is 12 cm, a right circular cylindrical cavity of height 3 cm and radius 4 cm is hollowed out such that bases of cone and cylinder form concentric circles. Find the surface area of the remaining solid in terms
Q) A farmer has a circular piece of land. He wishes to construct his house in the form of largest possible square within the land as shown below: The radius of circular piece of land is 35 m. Based on given information, answer the following questions: (i) Find the length of wire needed to fence
Q) From a solid cylinder of height 24 cm and radius 5 cm, two cones of height 12 cm and radius 5 cm are hollowed out. Find the volume and surface area of the remaining solid. PYQ: 34 (b) – CBSE 2025 – Code 30 – Series 5 – Set 1 Ans:Â Given that the
Q) From one of the faces of a solid wooden cube of side 14 cm, maximum number of hemispheres of diameter 1.4 cm are scooped out. Find the total number of hemispheres that can be scooped out. Also, find the total surface area of the remaining solid. PYQ: 34 (a) – CBSE 2025 – Code
      Q) In the given figure, and AB = 5 cm. Find the value of DC. [UP Board Exam paper, 2024] Ans: Step 1: Lets start with Δ AOB and Δ COD: If these triangles are similar, then: Since it is given that , Therefore, by SAS criterion of similarity, Δ
In the given figure, AO/OC=BO/OD=1/2 and AB = 5 cm. Find the value of DC. Read More »