Surface Areas a...

A solid sphere of radius $$x$$ cm is melted and recast into a shape of a solid cone of radius $$x$$ cm. The height of the cone is:

A sphere is melted and half of the molten liquid is used to form $$11$$ identical cubes, whereas the remaining half is used to form $$7$$ identical smaller spheres. The ratio of the side of the cube to the radius of the new small sphere is -

A metallic cube of edge $$1\ cm$$ is drawn into a wire of diameter $$4\ mm$$, then the length of the wire is:

The edges of three cubes of metal are $$3$$ cm, $$4$$ cm and $$5$$ cm. They are melted and formed in to a single cube. Find the edge of the new cube.

A cylindrical hut $$4$$ m tall and $$7$$ m in diameter is surmounted by aright circular cone of semi-vertical angle $$45$$ $$^{\circ}$$. The volume of air inside the hut is -

A drinking glass is in the shape of a frustum of a cone of height $$14\ cm$$. The diameters of its two circular ends are $$4\ cm$$ and $$2\ cm$$. Find the capacity of the glass.

STATEMENT - 1: The slant height of frustum of a cone is 4 cm. and perimeters of its circular ends are 18 cm. and 6 cm. then the curved surface area is 48 sq. cm.
STATEMENT - 2: Curved surface area of frustum $$ = \pi (r_1+r_2) $$, where $$r_1$$ and $$r_2$$ are radii of the frustum and $$l$$ is a slant height.

The given figure shows a solid formed of a solid cube of side 40 cm and a solid cylinder of radius 20 cm and height 50 cm attached to the cubes as shown. Find the volume and the total surface area of the whole solid [Take $$\pi \, =\, 3.14$$]

The given figure shows a solid formed of a solid cube of side $$40 cm$$ and a solid cylinder of radius $$20 cm$$ and height $$50 cm$$ attached to the cube as shown. Find the volume of the whole solid. $$\displaystyle \left [ Take\ \pi=3.14 \right ]$$.

A sphere of diameter 12.6 cm is melted and cast into a right circular cone of height 25.2 cm. The diameter base of the cone is