Sample QuestionsSurface Area And Volume of Sphere questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If a solid sphere of radius $10\ cm$ is moulded into $8$ spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is:
- ✓
$100\pi$
- B
$75\pi$
- C
$60\pi$
- D
$50\pi$
Answer: A.
View full solution →A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is:
- ✓
$1 : 2 : 3$
- B
$2 : 1 : 3$
- C
$2 : 3 : 1$
- D
$3 : 2 : 1$
Answer: A.
View full solution →The largest sphere is cut off from a cube of side $6\ cm$. The volume of the sphere will be:
- A
$27\pi\ \text{cm}^2$
- ✓
$36\pi\ \text{cm}^3$
- C
$108\pi\ \text{cm}^3$
- D
$12\pi\ \text{cm}^3$
Answer: B.
View full solution →A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is
Answer: C.
View full solution →The total surface area of a hemisphere of radius r is:
- A
$\pi\text{r}^2$
- B
$2\pi\text{r}^2$
- ✓
$3\pi\text{r}^2$
- D
$4\pi\text{r}^2$
Answer: C.
View full solution →Statement-1 (A): If a right circular cylinder just encloses a sphere, then surface area of the sphere is equal to the curved surface area of the cylinder.
Statement-2 (R): The volume of the largest sphere that can be inserted in a cube of edge a is $\frac{\pi a^3}{6}$.
- A
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-3
- ✓
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-3
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement-2 is True.
Answer: B.
View full solution →Statement-1 (A): If the surface areas of two spheres are in the ratio $9: 25$, then their radii are in the ratio $3: 5$.
Statement-2 (R) : If surface areas of two spheres are in the ratio $S_1: S_2$, then their radii are in the ratio $\sqrt{S_1}: \sqrt{S_2}$.
- ✓
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-2
- B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-2
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Statement-1 (A): If the ratio of volumes of two spheres is 27 : 64, then the ratio of their surface areas is 9 : 16.
Statement-2 (R): If $V_1, V_2$ are volumes and $S_1, S_2$ are surface areas of two spheres, then
$\frac{S_1}{S_2}=\left(\frac{V_1}{V_2}\right)^{2 / 3}$
- ✓
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1
- B
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1
- C
Statement-1 is True, Statement-2 is False.
- D
Statement-1 is False, Statement-2 is True.
Answer: A.
View full solution →Statement-1 (A): If the ratio of the surface areas of two spheres is 4: 25, then the ratio of their radii is 4: 5.
Statement-2 (R): If the ratio of radii of two spheres is 2: 3, then the ratio of their volumes is 8:27.
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- ✓
Statement-1 is false, Statement-2 is true.
Answer: D.
View full solution →Statement-1 (A): If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere is $6: \pi$.
Statement-2 (R): The volume of the largest right circular cone that can be fitted in a cube whose edge is 2r equals to the volume of a hemisphere of radius r.
- A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- ✓
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- C
Statement-1 is true, Statement-2 is false.
- D
Statement-1 is false, Statement-2 is true.
Answer: B.
View full solution →Fifteen identical spheres are made by melting a solid cylinder of radius 10 cm and height 5.4 cm, the diameter of each sphere is __________.
If a solid sphere of radius 4 cm is melted and recast into n solid hemispheres of radius 2 cm each, then n = __________.
If a solid hemisphere of radius 8 cm is melted and recast into n spheres of radius 2 cm each, then n= __________.
If the radius of a sphere is doubled, then the percentage increase in the surface area is __________.
A right circular cylinder and a sphere have the same volume and same radius. The ratio of the areas of their curved surfaces is __________.
Find the surface area of a sphere of diameter:$3.5\ cm$
View full solution →Find the volume of a sphere whose radius is: $2\ cm.$
View full solution →Find the surface area of a sphere of diameter:$21\ cm$
View full solution →Find the volume of a sphere whose radius is:$10.5\ cm.$
View full solution →Find the volume of a sphere whose radius is: $3.5\ cm$
View full solution →A cylinder of radius $12\ cm$ contains water to a depth of $20\ cm$. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by $6.75\ cm$. Find the radius of the ball. $\Big(\text{Use }\pi=\frac{22}{7}\Big).$
View full solution →A cone and a hemisphere have equal bases and equal volumes. Find the ratio of their heights.
A hemispherical tank has the inner radius of $2.8\ m$. Find its capacity in liters.
View full solution →A metallic sphere of radius $10.5\ cm$ is melted and thus recast into small cones, each of radius $3.5\ cm$ and height $3\ cm$. Find how many cones are obtained.
View full solution →A cylindrical jar of radius 6cm contains oil. Iron spheres each of radius $1.5\ cm$ are immersed in the oil. How many spheres are necessary to raise the level of the oil by two centimeters?
View full solution →The diameter of a copper sphere is $18\ cm$. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108m, find its diameter.
View full solution →How many spherical bullets can be made out of a solid cube of lead whose edge measures $44\ cm$, each bullet being 4cm in diameter?
View full solution →The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface areas.
A hemispherical bowl made of brass has inner diameter $10.5\ cm$. Find the cost of tin plating it on the inside at the rate of $Rs.$ $4$ per $100cm^2$
View full solution →A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is $17.6\ cm$, find the cost of painting it, given the cost of painting is Rs. $5$ per $100cm^2$
View full solution →A measuring jar of internal diameter $10\ cm$ is partially filled with water. Four equal spherical balls of diameter $2\ cm$ each are dropped in it and they sink down in water completely. What will be the change in the level of water in the jar?
View full solution →A sphere of radius $5\ cm$ is immersed in water filled in a cylinder, the level of water rises $\frac{5}{3}$cm. Find the radius of the cylinder.
View full solution →A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is $16\ cm$ and its height is $15\ cm$. Find the cost of painting the toy at $Rs.$ $7$ per $100cm^2$
View full solution →A spherical ball of lead $3\ cm$ in diameter is melted and recast into three spherical balls. If the diameters of two balls be $\frac{3}{2}$$cm$ and $2\ cm$, find the diameter of the third ball.
View full solution →A hollow sphere of internal and external radii $2\ cm$ and $4\ cm$ respectively is melted into a cone of base radius $4\ cm$. Find the height and slant height of the cone.
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