Surface Areas and Volumes: 1 mark Questions (CBSE Class 10)

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${}^2$

The total surface area of a solid hemisphere of diameter '$2d$' is :

1. (A)$3\pi d^2$
2. (B)$2\pi d^2$
3. (C)$\frac{1}{2}\pi d^2$
4. (D)$\frac{3}{4}\pi d^2$

The radius of a sphere (in cm) whose volume is $36\pi$ cm${}^3$, is :

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

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)$3140\sqrt{2}$ $c{m}^2$

A camping tent in hemispherical shape of radius 1.4 m, has a door opening of area 0.50 $m^2$. Outer surface area of the tent is

1. (A)11.78 $m^2$
2. (B)12.32 $m^2$
3. (C)11.82 $m^2$
4. (D)12.86 $m^2$

For which of the following solids is the lateral/curved surface area and total surface area the same ?

1. (A)Cube
2. (B)Cuboid
3. (C)Hemisphere
4. (D)Sphere

A cone and a cylinder have the same base radius and volume.
The (height of cone : height of cylinder) is :

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

A cone of height ‘h’ and radius ‘r’ is surmounted on a solid cylinder of same dimensions. The total surface area of the entire solid will be :

1. (A)$2\pi rh+\pi r\sqrt{h^2+r^2}$
2. (B)$2\pi rh+\pi r^2+\pi r\sqrt{h^2+r^2}$
3. (C)$2\pi rh+2\pi r^2+\pi r\sqrt{h^2+r^2}$
4. (D)$2\pi rh+\pi r\sqrt{h^2+r^2}-\pi r^2$

A cone of height ‘h’ and radius ‘r’ is surmounted on a hemisphere of same radius. The total surface area of the entire solid will be :

1. (A)$\pi rh+\pi r^2$
2. (B)$\pi r\sqrt{h^2+r^2}+\pi r^2$
3. (C)$\pi r\sqrt{h^2+r^2}+2\pi r^2$
4. (D)$\pi r\sqrt{h^2+r^2}+3\pi r^2$

A cone and cylinder have same height and same radius. The volume of the cone and the volume of the cylinder are in the ratio :

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

Two right circular cylinders of equal volumes have their heights in the ratio 1:2. The ratio of their radii is :

1. (A)$\sqrt{2}:1$
2. (B)1 : 2
3. (C)1 : 4
4. (D)$1:\sqrt{2}$

The curved surface area of a cone with base radius 7 cm, is 550 cm${}^2$. The slant height of the cone is :

1. (A)25 cm
2. (B)14 cm
3. (C)20 cm
4. (D)24 cm

The largest possible cone is just fitted inside a hollow cube of edge 25 cm. The radius of the base of the cone is

1. (A)5 cm
2. (B)12.5 cm
3. (C)25 cm
4. (D)10 cm

Assertion (A) : When a hemisphere of same radius (r) is carved out from one side of a solid wooden cylinder, the total surface area of remaining solid is increased by $2\pi r^2$.
Reason (R) : Curved surface area of hemisphere is $2\pi r^2$.

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.

Two identical cones are joined as shown in the figure. If radius of base is 4 cm and slant height of the cone is 6 cm, then height of the solid is

1. (A)8 cm
2. (B)$4\sqrt{5}$ cm
3. (C)$2\sqrt{5}$ cm
4. (D)12 cm

The volume of air in a hollow cylinder is 450 cm${}^3$. A cone of same height and radius as that of cylinder is kept inside it. The volume of empty space in the cylinder is

1. (A)225 cm${}^3$
2. (B)150 cm${}^3$
3. (C)250 cm${}^3$
4. (D)300 cm${}^3$

Assertion (A) : If we join two hemispheres of same radius along their bases, then we get a sphere.
Reason (R) : Total Surface Area of a sphere of radius $r$ is $3\pi r^2$.

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.

If the volumes of two cubes are in the ratio $8:125$, then the ratio of their surface areas is :

1. (A)$8:125$
2. (B)$4:25$
3. (C)$2:5$
4. (D)$16:25$

The radii 'r' of a sphere and that of the base of a cone are same. If their volumes are also same, then the height of the cone is :

1. (A)$r$
2. (B)$2r$
3. (C)$3r$
4. (D)$4r$

On the top face of the wooden cube of side 7 cm, hemispherical depressions of radius 0.35 cm are to be formed by taking out the wood. The maximum number of depressions that can be formed is :

1. (A)400
2. (B)100
3. (C)20
4. (D)10

A cone of height 12 cm and slant height 13 cm is surmounted on a hemisphere having radius equal to that of cone. The entire height of the solid is

1. (A)17 cm
2. (B)18 cm
3. (C)22 cm
4. (D)23 cm

If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of remaining wood to the volume of cone hollowed out is

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

The height and radius of a right circular cone are 24 cm and 7 cm respectively. The slant height of the cone is :

1. (A)24 cm
2. (B)31 cm
3. (C)26 cm
4. (D)25 cm

Outer surface area of a cylindrical juice glass with radius 7 cm and height 10 cm, is :

1. (A)440 sq m
2. (B)594 sq m
3. (C)748 sq m
4. (D)1540 sq m

The radius of a sphere is $\frac{7}{2}$ cm. The volume of the sphere is :

1. (A)$\frac{231}{3}$ cu cm
2. (B)$\frac{539}{12}$ cu cm
3. (C)$\frac{539}{3}$ cu cm
4. (D)154 cu cm

The total surface area of a solid hemisphere of radius 7 cm is :

1. (A)$98\pi$ cm${}^2$
2. (B)$147\pi$ cm${}^2$
3. (C)$196\pi$ cm${}^2$
4. (D)$228\frac{2}{3}\pi$ cm${}^2$

The total surface area of a cube of side 20 cm is

1. (A)240 cm${}^2$
2. (B)160 cm${}^2$
3. (C)2400 cm${}^2$
4. (D)1600 cm${}^2$

If the volume of a sphere is $\frac{11}{21}$ cm${}^3$, then the radius of the sphere is :

1. (A)2 cm
2. (B)4 cm
3. (C)$\frac{1}{2}$ cm
4. (D)$\frac{1}{4}$ cm

From a solid cube of side 14 cm, a sphere of maximum diameter is carved out. The radius of sphere is :

1. (A)7 cm
2. (B)14 cm
3. (C)$\frac{7}{2}$ cm
4. (D)$\sqrt{14}$ cm

A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is :

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

The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is :

1. (A)$\frac{4\pi }{3}$ cu cm
2. (B)$\frac{5\pi }{3}$ cu cm
3. (C)$\frac{8\pi }{3}$ cu cm
4. (D)$\frac{2\pi }{3}$ cu cm

Assertion (A) : Two cubes each of edge length 10 cm are joined together. The total surface area of newly formed cuboid is 1200 cm${}^2$.
Reason (R) : Area of each surface of a cube of side 10 cm is 100 cm${}^2$.

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

The ratio of total surface area of a solid hemisphere to the square of its radius is :

1. (A)$2\pi :1$
2. (B)$4\pi :1$
3. (C)$3\pi :1$
4. (D)$1:4\pi$

Two identical solid cubes of side ‘a’ are joined end-to-end. The total surface area of the resulting cuboid is :

1. (A)$6a^2$
2. (B)$10a^2$
3. (C)$5a^2$
4. (D)$4a^2$

The volume of a cone of radius ‘r’ and height ‘3r’ is :

1. (A)$\frac{1}{3}\pi r^3$
2. (B)$3\pi r^3$
3. (C)$9\pi r^3$
4. (D)$\pi r^3$

The curved surface area of a right circular cylinder of height 14 cm is 88 cm${}^2$. The diameter of its circular base is :

1. (A)2 cm
2. (B)1 cm
3. (C)4 cm
4. (D)7 cm

A solid is of the form of a cone of radius ‘r’ surmounted on a hemisphere of the same radius. If the height of the cone is the same as the diameter of its base, then the volume of the solid is :

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

The curved surface area of a cone of radius 7 cm is 550 cm${}^2$. Its slant height is :

1. (A)24 cm
2. (B)25 cm
3. (C)14 cm
4. (D)20 cm

Assertion (A) : The surface area of largest sphere that can be inscribed in a hollow cube of side ‘a’ cm is $\pi a^2$ cm${}^2$.
Reason (R) : The surface area of a sphere of radius ‘r’ is $\frac{4}{3}\pi r^3$.

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.

Curved surface area of a cylinder of height 5 cm is 94.2 cm${}^2$. Radius of the cylinder is (Take $\pi =3.14$)

1. (A)2 cm
2. (B)3 cm
3. (C)2.9 cm
4. (D)6 cm

The curved surface area of a cone having height 24 cm and radius 7 cm, is

1. (A)528 cm${}^2$
2. (B)1056 cm${}^2$
3. (C)550 cm${}^2$
4. (D)500 cm${}^2$

The area of metal sheet required to make a closed hollow cylinder of height 2.4 m and base radius 0.7 m, is

1. (A)10.56 m${}^2$
2. (B)13.52 m${}^2$
3. (C)13.64 m${}^2$
4. (D)14.08 m${}^2$

What is the total surface area of a solid hemisphere of diameter ‘d’ ?

1. (A)$3\pi d^2$
2. (B)$2\pi d^2$
3. (C)$\frac{1}{2}\pi d^2$
4. (D)$\frac{3}{4}\pi d^2$

If the area of the base of a cone is 51 cm² and its volume is 85 cm³, then the vertical height of the cone is given as :

1. (A)$\frac{5}{6}$ cm
2. (B)$\frac{5}{3}$ cm
3. (C)$\frac{5}{2}$ cm
4. (D)5 cm

Water in a river which is 3 m deep and 40 m wide is flowing at the rate of 2 km/h. How much water will fall into the sea in 2 minutes ?

1. (A)800 m${}^3$
2. (B)4000 m${}^3$
3. (C)8000 m${}^3$
4. (D)2000 m${}^3$

The volume of a right circular cone whose area of the base is 156 cm${}^2$ and the vertical height is 8 cm, is

1. (A)2496 cm${}^3$
2. (B)1248 cm${}^3$
3. (C)1664 cm${}^3$
4. (D)416 cm${}^3$