Surface Areas and Volumes: CBSE Class 10 Previous Year Questions

Two wooden solid hemispheres of same radii r, are joined at a point, as shown in the figure. The total surface area of the object is :

1. (A)$4\pi r^2$
2. (B)$6\pi r^2$
3. (C)$3\pi r^2$
4. (D)$5\pi r^2$

A cone with slant height 10 cm and radius 6 cm is surmounted on a hemisphere of same radius. The height of the toy is :

1. (A)12 cm
2. (B)16 cm
3. (C)14 cm
4. (D)10 cm

A cylinder of radius $r$ is surmounted on a hemisphere of same radius. If total height of the object is 13 cm, then its inner surface area is

1. (A)$2\pi r(r+13)$
2. (B)$13\pi r$
3. (C)$2\pi (13+r{)}^2$
4. (D)$26\pi r$

The total surface area of a solid cone of radius 7 cm and slant height 25 cm, is

1. (A)724 cm${}^2$
2. (B)704 cm${}^2$
3. (C)550 cm${}^2$
4. (D)616 cm${}^2$

A hemispherical bowl is made of steel of thickness 1 cm. The outer radius of the bowl is 6 cm. The volume of steel used (in $c{m}^3$) is :

1. (A)$182\pi$
2. (B)$\frac{182}{3}\pi$
3. (C)$\frac{682}{3}\pi$
4. (D)$\frac{364}{3}\pi$

Assertion (A) : The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is 160 $c{m}^2$.
Reason (R): The surface area of a cuboid of dimensions $l\times b\times h$ is $(lb+bh+hl)$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

A cone of maximum size is carved out from a solid cube of edge length $l$. The volume of the cone is :

1. (A)$\frac{\pi l^3}{12}$
2. (B)$\frac{\pi l^3}{3}$
3. (C)$l^3\left(1-\frac{\pi }{3}\right)$
4. (D)$\frac{\pi l^3}{8}$

Three tennis balls are just packed in a cylindrical jar. If radius of each ball is r, volume of air inside the jar is

1. (A)$2\pi r^3$
2. (B)$3\pi r^3$
3. (C)$5\pi r^3$
4. (D)$4\pi r^3$

An ice-cream cone of radius r and height h is completely filled by two spherical scoopes of ice-cream. If radius of each spherical scoop is $\frac{r}{2}$, then h : 2r equals

1. (A)1 : 8
2. (B)1 : 2
3. (C)1 : 1
4. (D)2 : 1

A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius 10 cm. Curved surface area of the cavity carved out is (use $\pi =3.14$)

1. (A)$314\sqrt{2}$ $c{m}^2$
2. (B)314 $c{m}^2$
3. (C)$\frac{3140}{3}$ $c{m}^2$
4. (D)$3140\sqrt{2}$ $c{m}^2$