Formulae [1]
Formula: Standard Combinations
Cylinder + Two Hemispheres
TSA = CSA of cylinder + 2 × CSA of hemisphere
Cone + Hemisphere
TSA = CSA of cone + CSA of hemisphere
Cube + Hemisphere
TSA = TSA of cube − area of circular base + CSA of hemisphere
Key Points
Key Points: Volume of a Combination of Solids
Volume is always conserved:
Volume of combination = Sum of volumes of all parts
Hollow / Reduced Capacity Solids:
Actual volume = Apparent volume − Volume of hollow part
Important Questions [41]
- Due to sudden floods, some welfare associations jointly requested the government to get 100 tents fixed immediately and offered to contribute 50% of the cost. If the lower part of each tent is of the form of a cylinder of diameter 4.2 m and height 4 m with the conical upper part of same diameter but of height 2.8 m
- A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of each bottle, if 10% liquid is wasted in this transfer.
- A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed,
- 504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere. Find the diameter of the sphere and hence find its surface area.
- If the total surface area of a solid hemisphere is 462 cm^2 , find its volume.
- The Largest Possible Sphere is Carved Out of a Wooden Solid Cube of Side 7 Em. Find The Volume of the Wood Left
- Water in a canal, 6 m wide and 1.5 m deep, is flowing at a speed of 4 km/h. How much area will it irrigate in 10 minutes, if 8 cm of standing water is needed for irrigation?
- In Figure 2, ABCD is a trapezium of area 24.5 sq. cm. In it, AD|| BC, ∠ DAB = 900, AD = 10 cm and BC = 4 cm. If ABE is a quadrant of a circle, find the area of the shaded region. [Take π=22/7]
- 150 spherical marbles, each of diameter 1.4 cm, are dropped in a cylindrical vessel of diameter 7 cm containing some water, which are completely immersed in water. Find the rise in the level of
- In Fig. 5, is a decorative block, made up two solids – a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on the top has diameter of 3.5 cm. Find the total surface area of the bock
- The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder.
- A right circular cone of radius 3 cm, has a curved surface area of 47.1 cm2. Find the volume of the cone.
- A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the top (Use π = 22/7)
- The Number of Solid Spheres, Each of Diameter 6 Cm that Can Be Made by Melting a Solid Metal Cylinder of Height 45 Cm and Diameter 4 Cm, is
- In Fig. 4, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid.
- A Solid Wooden Toy is in the Form of a Hemisphere Surrounded by a Cone of Same Radius. the Radius of Hemisphere is 3.5 Cm and the Total Wood Used in the Making of Toy is 1
- In Fig. 5, from a cuboidal solid metallic block, of dimensions 15cm ✕ 10cm ✕ 5cm, a cylindrical hole of diameter 7 cm is drilled out. Find the surface area of the remaining block
- From a solid cylinder of height 2.8 cm and diameter 4.2 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid [take π=22/7]
- A Toy is in the Form of a Cone of Radius 3.5 Cm Mounted on a Hemisphere of Same Radius. the Total Height of the Toy is 15.5 Cm. Find the Total Surface Area of the to
- A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in given figure. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm
- Water in a Canal, 5·4 M Wide and 1·8 M Deep, is Flowing with a Speed of 25 Km/Hour. How Much Area Can It Irrigate in 40 Minutes, If 10 Cm of Standing Water is Required for Irrigation?
- From a Solid Right Circular Cylinder of Height 2.4 Cm and Radius 0.7 Cm, a Right Circular Cone of Same Height and Same Radius is Cut Out. Find the Tota
- Find the Area of the Shaded Region in Fig. 3, Where Arcs Drawn with Centres A, B, C and D Intersect in Pairs at Mid-points P, Q, R and S of the Sides Ab, Bc, Cd and Da Respectively of a Square Abcd of Side 12 Cm. [Use π = 3.14]
- The Diameters of the Lower and Upper Ends of a Bucket in the Form of a Frustum of a Cone Are 10 Cm and 30 Cm Respectively. If Its Height is 24 Cm, Find:
- A Cylindrical Tub, Whose Diameter is 12 Cm and Height 15 Cm is Full of Ice-cream. the Whole Ice-cream is to Be Divided into 10 Children in Equal Ice-cream Cones,
- A Metallic Cylinder Has Radius 3 Cm and Height 5 Cm. to Reduce Its Weight, a Conical Hole is Drilled in the Cylinder. the Conical Hole Has a Radius of 3 2 Cm and Its Depth is 8 9 Cm.
- In Figure 4, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off.
- A Vessel is in the Form of Hemispherical Bowl Surmounted by a Hollow Cylinder of Same Diameter. the Diameter of the Hemispherical Bowl is 14 Cm and the Total Height of the Vessel is 13 Cm.
- If the Radius of the Base of a Right Circular Cylinder is Halved, Keeping the Height the Same, Then the Ratio of the Volume of the Cylinder Thus Obtained to the Volume of Original Cylinder Is:
- In Fig. 6, Oabc is a Square of Side 7 Cm. If Oapc is a Quadrant of a Circle with Centre O, Then Find the Area of the Shaded Region. [ U S E R = 22 7 ]
- From a Solid Cylinder of Height 7 Cm and Base Diameter 12 Cm, a Conical Cavity of Same Height and Same Base Diameter is Hollowed Out. Find the Total Surface Area of the Remaining Solid. [User π 22 7 ]
- Two Cubes Each of Volume 27 Cm3 Are Joined End to End to Form a Solid. Find the Surface Area of the Resulting Cuboid.
- A Bucket Open at the Top is in the Form of a Frustum of a Cone with a Capacity of 12308.8 Cm3. the Radii of the Top and Bottom of the Circular Ends of the Bucket Are 20 Cm and 12 Cm Respectively.
- A Cone of Height 24 Cm and Radius of Base 6 Cm is Made up of Modelling Clay. a Child Reshapes It in the Form of a Sphere. Find the Radius of the Sphere and Hence Find the Surface Area of this Sphere.
- A Container Opened at the Top and Made up of a Metal Sheet, is in the Form of a Frustum of a Cone of Height 16 Cm with Radii of Its Lower and Upper Ends as 8 Cm and 20 Cm Respectively.
- The total surface area of a solid hemisphere of radius 7 cm is ______.
- Read the following passage and answer the questions given below. Khurja is a city in the Indian state of Uttar Pradesh famous for the pottery.
- 3 cubes each of 8 cm edge are joined end to end. Find the total surface area of the cuboid.
- The boilers are used in thermal power plants to store water and then used to produce steam. One such boiler consists of a cylindrical part in middle and two hemispherical parts at its both ends.
- The ratio of total surface area of a solid hemisphere to the square of its radius is ______.
- Tamper-proof tetra-packed milk guarantees both freshness and security. This milk ensures uncompromised quality, preserving the nutritional values within and making it a reliable choice for health
