ind below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Surface Areas and Volumes:

Exercise 12.3 (Q. No. 1-7)

Question. 1 Three metallic solid cubes whose edges are 3cm, 4cm and 5cm are melted and formed into a single cube. Find the edge of the cube so formed.

Solution.

Given, edges of three solid cubes are 3cm, 4cm and 5cm, respectively.

So, volumes of of three solid cubes are (3)³, (4)³ and (5)³ = 27cm³, 64cm³ and 125cm³, respectively.

Now, Since volume of resulting cube = Sum of volume of three cubes = (27 + 64+ 125) = 216cm³

Let R be the edge of the resulting cube

⟹           R³ =216

⟹           R = 6cm

Hence, the edge of new cube is 6 cm.

Question. 2 How many shots each having diameter 3cm can be made from a cuboidal Lead solid of dimensions 9cm × 11cm × 12cm?

Solution.              

Question. 3 A bucket is in the form of a frustum of a cone and holds 28.490 L of water. The radii of the top and bottom are 28cm and 21cm, respectively. Find the height of the bucket.

Solution.

Question. 4 A cone of radius 8cm and height 12cm is divided into two parts by a plane through the mid-point of its axis parallel to its base. Find the ratio of the volumes of two parts.

Solution.

Let ABC be the given cone with radius 8cm and height 12cm.

Question. 5 Two identical cubes each of volume 64 cm³ are joined together end to end. What is the surface area of the resulting cuboid?

Solution.

Question. 6   From a solid cube of side 7cm, a conical cavity of height 7cm and radius 3cm is hollowed out. Find the volume of the remaining solid.

Solution.

Question. 7 Two cones with same base radius 8cm and height 15cm are joined together along their bases. Find the surface area of the shape so formed.

Solution.

When two identical cones are joined base to base, the total surface area of new solid becomes equal to the sum of curved surface areas of both the cones.

Given, radius of each cone, r = 8cm

And height of each cone, h = 15 cm

CBSE Class 10 NCERT Textbooks & NCERT Solutions