Exercise 12.2: Volume of Combined Solids
Find the volume of combined solids. Unlike surface area, volume is simply additive — just add the volumes of each part.
Extra Practice Questions
These questions cover the same concepts as Exercise 12.2. Try solving them to build confidence before or after the textbook exercise.
A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted to form a solid cone of base diameter 8 cm. What is the height of the cone?
Ravi was calculating the curved surface area of a solid formed by a cylinder with a conical depression at one end. He used the formula 'CSA_cylinder + CSA_cone'. Which of the following statements is TRUE regarding his approach?
A solid right circular cylinder of height 'H' and radius 'R' is melted and recast into 'N' identical cones, each of height 'h' and radius 'r'. If h = H/2 and r = R/2, what is the value of N?
A decorative block is made of two solids: a cube and a hemisphere. The base of the block is a cube with edge length 5 cm, and the hemispherical part is fixed on the top of the cube. If the diameter of the hemisphere is 4.2 cm, find the total surface area of the block. (Use π = 22/7)
A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment. (Use π = 22/7)
A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the conical top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas if it costs ₹500 per m². (Use π = 22/7)
A cylindrical bucket, 32 cm high and with a radius of base 18 cm, is full of sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius of the base of the heap.
A solid is composed of a cylinder with hemispherical ends. If the total length of the solid is 108 cm and its total surface area is 4752 cm², find the radius of the hemispherical ends. (Take π = 22/7)
A toy is in the shape of a cone mounted on a hemisphere of the same base radius. Which expression correctly represents the total surface area of the toy?
If the radius of a solid metallic sphere is tripled, how many times will its volume increase compared to the original volume?
Stuck on a question?
Paste any question from Exercise 12.2 into our AI Maths Solver and get a step-by-step solution instantly. It works for all NCERT questions.
Try AI Solver — FreeCommon Mistakes to Avoid
- ✗Using surface area formulas instead of volume formulas
- ✗Not converting units when dimensions are in different units
- ✗Forgetting that volume = sum of volumes for combined solids
Other Exercises in Chapter 12
Frequently Asked Questions
How many questions are in Exercise 12.2?
Exercise 12.2 has 8 questions on volumes of combined solids.
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