Define Volume in Mathematics. And what is the formula for volume of combination of solids

Volume of Cone :  πr2h / 3

Volume of Cuboid : l x b x h

Volume of cube : a x a x a = a3

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Q. There is a 8 cm long cylindrical tank having 4 cm high conical shape over it with same base of radius of 3cm. Find the volume of the tank.

Ans: Height of cone (h2)= 4 cm Height of cylinder (h1)= 8 cm and radius (r)= 3 cm Volume of tank = V of cylinder + V of cone V = πr2h1  +   πr2h2 / 3  &nbs... read more

Q. A medicine capsule is in the shape of cylinder with two hemisphere stuck to each other at its ends.The length of the entire capsule is 14 mm and the diameter is of the capsule is 5mm. Find its volume.

Ans: Height of cylinder(h)= 14 – 5 = 9 mm radius of cylinder ( r ) = 5/2 radius of hemisphere ( r ) = 5/2 Volume of capsule = V of cylinder + V of both hemisphere V = πr2h + 2 x (2/3)&p... read more

Q. How many cubes of edge 2 cm can be made out of a solid cuboid of dimensions 16cm x 12cm x 10cm

Ans: Length of the cuboid l = 16cm Breadth of the cuboid b = 12cm Height of the cuboid h = 10cm volume of the cuboid = l × b × h                 &nbs... read more

Q. A solid is of the shape of a cone standing on a hemisphere with a common base of radius equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid.

Ans: Radius of the cone  = 1cm Height of the cone = 1cm Radius of the hemisphere  = 1cm Volume of the solid = volume of the cone + volume of the hemisphere V = πr2h /... read more

Q. A field is in the form of rectangle of length 20 m and width 14 m. A 10 m deep well of diameter 7 m is dug in one corner of the field and the earth taken out of the well is spread evenly over the remaining part of the field. Find the rise in the level of the field.

Ans: According to the question- volume of earth level rise in the field = volume of well    ---------------(1) Length of field is l = 20 m Width of field is b = 14 m Let h is the level rise... read more

Q. 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 cylinder is 7 cm. Find the total volume of the solid.

Ans: Given diameter of the cylinder is = 7 cm As radius of the cylinder = radius of the hemisphere So r is 7/2 = 3.5 cm Given height of the solid is 20 cm So height of the cylinder is = 20 - 2(3.5) =... read more

Q. The curved surface area of a cylinder is 264 m2 and its volume is 924 m3. Find the ratio of its height to its diameter.

Ans: Curved Surface Area of the cylinder = 2πrh So 2πrh = 264 m2    ----------------------(1) Volume of the cylinder = πr2h So πr2h = 924 m3     ------------------... read more

Q. A rectangular sheet of paper 40cm × 22cm is rolled to form a hollow cylinder of height 40 cm. Find the radius of the cylinder.

Ans: Here, Height of cylinder h = 40cm, circumference = 22cm when the sheet is rolled then bredth of rectangular sheet i.e. 22 cm becomes the circumference of the base circle. As circumference of ci... read more

Q. A solid metallic cuboid 24cm X 11cm X 7cm is melted and recast into solid cones of base radius 3.5 cm and height 6 cm. Find the number of cones so formed.

Ans: As dimensions of metallic cuboid = 24cm × 11cm × 7cm Base radius of cone = 3.5 cm And Height of cone = 6 cm Let n be the number of cones formed. Now, according to question volume... read more

Q. A cylinder, a cone and a hemisphere have same base and same height. Find the ratio of their volumes.

Ans: Volume of cylinder = πr2h Volume of cone = (1/3)πr2h Volume of hemisphere = (2/3)πr3 Volume of cylinder : Volume of cone : Volume of hemisphere   = πr2h : (1/3)πr2h : (2/3)&p... read more

Q. Two cubes each of volume 8 cm3 are joined end to end, then what is the surface area of resulting cuboid.

Ans: As volume of each cube is 8 cm3 Now side of cube is = ∛8 = 2 cm As both cubes are joined end to end. So the dimensions of the resulting cuboid are Length of cuboid l = 2 + 2 = 4 cm Breadth b = 2... read more

Q. The radius of sphere is r cm. It is divided into two equal parts. Find the whole surface of two parts.

Ans: Radius of a sphere = r cm As the sphere is divided into two equal parts, then the resulting parts are hemispheres with radius r cm. Whole surface of each part =2πr2 + πr2 = 3πr2 Total ... read more

Q. What is the volume of a right circular cylinder of base radius 7 cm and height 10 cm ? Use π=22/7

Ans: Radius of right circular cylinder = 7 cm Height of right circular cylinder = 10 cm Volume of right circular cylinder = πr2h = (22/7) x 7 x 7 x 10 = 1540 cm3... read more

Q. The volume of a cuboid is 180 cm3. The base is a square of side length 6 cm. Calculate the height of this cuboid.

Ans: As base of the cuboid is square. So two sides will be 6cm long as given. let h is the height of cuboid. Now volume is = 180 6 x 6 x h = 180 36h = 180 h = 180/36 h = 5 Hence Calculated ... read more