Surface Areas and Volumes

CBSE Class 10 Mathematics · every board question from this chapter, 2022–2026

• A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius 10 cm. Curved surface area of the…2026
• A cone of maximum size is carved out from a solid cube of edge length l. The volume of the cone is:2026
• In the given figure, AB ∥ EF. If AB=24 cm, EF=36 cm and DA=7 cm, then AE equals2026
• A camping tent in hemispherical shape of radius 1.4 m, has a door opening of area 0.50 m^2. Outer surface area of the tent is2026
• Three tennis balls are just packed in a cylindrical jar. If radius of each ball is r, volume of air inside the jar is2026
• The radius of a sphere (in cm) whose volume is 36 π cm^3, is:2026
• In the given figure, PQ ∥ YZ such that XP: PY=2: 3. If PQ=5 cm, then YZ equals2026
• The total surface area of a solid hemisphere of diameter ' 2 d ' is:2026
• A hemispherical bowl is made of steel of thickness 1 cm. The outer radius of the bowl is 6 cm. The volume of steel used (in cm^3…2026
• An ice-cream cone of radius r and height h is completely filled by two spherical scoopes of ice-cream. If radius of each…2026
• Assertion: The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is 160 cm^2. Reason (R):…2026
• 1000 small thermocol balls of radius 0•5 cm are kept in a spherical balloon of radius 20 cm. Find the volume of air in the…2026
• A toy is in the form of a cone mounted on a hemisphere of radius 7 cm. The total height of the toy is 31 cm. Find the total…2026
• A circle of diameter 20 cm is equally divided into five sectors. Find the area and perimeter of one of the sectors.2026
• A right circular cylinder and a right circular cone have equal bases and equal heights. If their curved surface areas are in the…2026
• To protect plants from heat, a shed of iron rods covered with green cloth is made. The lower part of the shed is a cuboid mounted…2026
• A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 20 cm and the diameter of the…2026
• A person on a tour has ₹ 4,200 for expenses. If he extends his tour for 3 days, he has to cut down his daily expenses by ₹ 70.…2026
• Two water taps together can fill a tank in 8 8/9 hours. The tap of larger diameter takes 4 hours less than the smaller one to…2026
• On a Sunday your parents took you to a fair. You could see lot of toys displayed and you wanted them to buy a Rubik's cube and a…2026
• A wall mounted lamp, made of fabric, is shown below. Lamp has cuboidal shape, open from top and bottom. A spherical bulb of…2026
• A wall mounted lamp, made of fabric, is shown below. Lamp has cuboidal shape, open from top and bottom. A spherical bulb of…2026
• A model of Leafy Ball Fountain is made to be kept on the tabletop. Water gently cascades down the ball into a decorative…2026
• On a Sunday your parents took you to a fair. You could see lot of toys displayed and you wanted them to buy a Rubik's cube and a…2026
• The radii 'r' of a sphere and that of the base of a cone are same. If their volumes are also same, then the height of the cone is:2025
• On the top face of the wooden cube of side 7 cm, hemispherical depressions of radius 0.35 cm are to be formed by taking out the…2025
• If the volumes of two cubes are in the ratio 8: 125, then the ratio of their surface areas is:2025
• If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of remaining…2025
• A cone of height 12 cm and slant height 13 cm is surmounted on a hemisphere having radius equal to that of cone. The entire…2025
• Assertion: If we join two hemispheres of same radius along their bases, then we get a sphere. Reason (R): Total Surface Area of a…2025
• If the radii of the bases of a cylinder and a cone are in the ratio 3: 4 and their heights are in the ratio 2: 3, find the ratio…2025
• A room is in the form of a cylinder surmounted by a hemispherical dome. The base radius of the hemisphere is half of the height…2025
• A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter…2025
• A bat manufacturing company made a huge bat for charity and got it signed by world cup winning team. The dimensions of the bat…2025
• Fermentation tanks are designed in the form of cylinder mounted on a cone as shown below: The total height of the tank is 3.3 m…2025
• On the day of her examination, Riya sharpened her pencil from both ends as shown below: The diameter of the cylindrical and…2025
• A wooden cubical die is formed by forming hemispherical depressions on each face of the cube such that face 1 has one depression,…2025
• From one face of a solid cube of side 14 cm, the largest possible cone is carved out. Find the volume and surface area of the…2025
• 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.…2025
• A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled…2025
• In order to provide shelter to flood victims, a shed was constructed using tin sheets which is in the form of cuboid surmounted…2025
• A skilled carpenter decided to craft a special rolling pin for the local baker. He carefully joined three cylindrical pieces of…2025
• Two identical solid cubes of side 'a' are joined end-to-end. The total surface area of the resulting cuboid is:2024
• The ratio of total surface area of a solid hemisphere to the square of its radius is:2024
• A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together,…2024
• The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is:2024
• Assertion: Two cubes each of edge length 10 cm are joined together. The total surface area of newly formed cuboid is 1200 cm^2.…2024
• The inner and outer radii of a hollow cylinder surmounted on a hollow hemisphere of same radii are 3 cm and 4 cm respectively. If…2024
• A wooden toy is made by scooping out a hemisphere of same radius as of cylinder, from each end of a wooden solid cylinder. If the…2024
• The difference between the outer and inner radii of a hollow right circular cylinder of length 14 cm is 1 cm. If the volume of…2024
• A tent is in the shape of a cylinder, surmounted by a conical top. If the height and diameter of the cylindrical part are 3.5 m…2024
• A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height…2024
• A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the…2024
• A solid iron pole consists of a solid cylinder of height 200 cm and base diameter 28 cm, which is surmounted by another cylinder…2024
• A juice seller was serving his customers using glasses as shown in the figure. The inner diameter of the cylindrical glass was 5…2024
• The word 'circus' has the same root as 'circle'. In a closed circular area, various entertainment acts including human skill and…2024
• Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the…2024
• The area of metal sheet required to make a closed hollow cylinder of height 2.4 m and base radius 0.7 m, is2023
• If the area of the base of a cone is 51 cm^2 and its volume is 85 cm^3, then the vertical height of the cone is given as:2023
• Water in a river which is 3 m deep and 40 m wide is flowing at the rate of 2 km / h. How much water will fall into the sea in 2…2023
• What is the total surface area of a solid hemisphere of diameter 'd'?2023
• Curved surface area of a cylinder of height 5 cm is 94.2 cm^2. Radius of the cylinder is (Take π=3.14 )2023
• The curved surface area of a cone having height 24 cm and radius 7 cm, is2023
• The volume of a right circular cone whose area of the base is 156 cm^2 and the vertical height is 8 cm, is2023
• A car has two wipers which do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of 120°. Find the…2023
• A room is in the form of cylinder surmounted by a hemi-spherical dome. The base radius of hemisphere is one-half the height of…2023
• From a solid cylinder of height 20 cm and diameter 12 cm, a conical cavity of height 8 cm and radius 6 cm is hallowed out. Find…2023
• A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in the figure. If the height…2023
• A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of them being 7 cm and the height…2023
• A student was asked to make a model shaped like a cylinder with two cones attached to its ends by using a thin aluminium sheet.…2023
• A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the…2023
• A golf ball is spherical with about 300-500 dimples that help increase its velocity while in play. Golf balls are traditionally…2023
• In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and height 14 cm and the…2023
• A solid metallic sphere of radius 10 · 5 cm is melted and recast into a number of smaller cones, each of radius 3.5 cm and height…2022
• A solid piece of metal in the form of a cuboid of dimensions 11 cm × 7 cm × 7 cm is melted to form 'n' number of solid spheres of…2022
• A cone of height 28 cm and radius of base 7 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find…2022
• 150 spherical marbles, each of diameter 1 · 4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, and…2022
• 150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, and…2022
• The curved surface area of a right circular cylinder is 176 sq cm and its volume is 1232 cu cm. What is the height of the…2022
• From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and same radius is hollowed out. Find the…2022
• From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and same radius is hollowed out. Find the…2022
• In Figure 2, from a solid cube of side 7 cm, a cylinder of radius 2 · 1 cm and height 7 cm is scooped out. Find the total surface…2022
• Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian pottery work…2022
• Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery. Khurja pottery is traditional Indian pottery work…2022
• Case Study - 2 A 'circus' is a company of performers who put on shows of acrobats, clowns etc. to entertain people started around…2022

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