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 […]
surface areas and volumes
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: 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 »
Q) Both the ends of a metallic solid cylinder are semi-spherical. Its total height is 19 cm and diameter of the cylinder is 7 cm. Find the weight of the solid if weight of 1 cm³ of the metal is 4.5 g. Ans: Step 1: Let’s make diagram for our
Q) Find the number of bricks, each measuring 25 cm x 12.5 cm x 7.5 cm, required to construct a wall 24 m long, 20 m high and 0.5 m thick while the cement and sand mixture occupies 1/20th of the volume of the wall. Ans: [Approach: A wall consists of bricks and sand-cement mixture.
Q) A cone and a cylinder have the same base radius and height. If the volume of the cylinder is 300 cm 3, find the volume of the cone. Ans: [Approach: Given that the radius and height are the same, we will find a relation of r and h from
Q) Rinku was very happy to receive a fancy jumbo pencil from his best friend Rohan on his birthday. Pencil is a basic writing tool, when sharpened its shape is a combination of cylinder & cone as given in the picture. Cylindrical pencil with conical head is a common shape worldwide since ages. Commonly pencils are
Q) In the adjoining diagram, 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 is placed vertically on a horizontal