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Surface Area And Volume of Sphere Maths - Surface Area And Volume of Sphere

Maharashtra Board - STD 9 - Maths (MSBSHSE - English Medium). 78 questions in this chapter.

Question types

Surface Area And Volume of Sphere question types

78 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

78
Questions
5
Question groups
5
Question types
Sample Questions

Surface 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.

Q 1MCQ(1M)1 Mark
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.

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Q 2MCQ(1M)1 Mark
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.

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Q 3MCQ(1M)1 Mark
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.

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Q 4MCQ(1M)1 Mark
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
  • A
    $4\pi\text{r}^3$
  • B
    $\frac{8}{3}\pi\text{r}^3$
  • ✓
    $2\pi\text{r}^3$
  • D
    $8\pi\text{r}^3$

Answer: C.

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Q 5MCQ(1M)1 Mark
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.

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Q 112 Mark Question2 Marks
A cylinder of radius 12cm contains water to a depth of 20cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75cm. Find the radius of the ball. $\Big(\text{Use }\pi=\frac{22}{7}\Big).$
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Q 142 Mark Question2 Marks
A metallic sphere of radius 10.5cm is melted and thus recast into small cones, each of radius 3.5cm and height 3cm. Find how many cones are obtained.
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Q 152 Mark Question2 Marks
A cylindrical jar of radius 6cm contains oil. Iron spheres each of radius 1.5cm are immersed in the oil. How many spheres are necessary to raise the level of the oil by two centimeters?
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Q 163 Mark Question3 Marks
The diameter of a copper sphere is 18cm. 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.
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Q 193 Mark Question3 Marks
A hemispherical bowl made of brass has inner diameter $10.5cm$. Find the cost of tin plating it on the inside at the rate of $Rs. 4$ per $100cm^2$​​​​​​​
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Q 203 Mark Question3 Marks
A hemispherical dome of a building needs to be painted. If the circumference of the base of the dome is $17.6cm$, find the cost of painting it, given the cost of painting is $Rs. 5$ per $100cm^2$
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Q 214 Mark Question4 Marks
A measuring jar of internal diameter 10cm is partially filled with water. Four equal spherical balls of diameter 2cm 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?
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Q 224 Mark Question4 Marks
A sphere of radius 5cm is immersed in water filled in a cylinder, the level of water rises $\frac{5}{3}$cm. Find the radius of the cylinder.
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Q 234 Mark Question4 Marks
A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is $16cm$ and its height is $15cm.$
Find the cost of painting the toy at $Rs. 7$ per $100cm^2$
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Q 244 Mark Question4 Marks
A spherical ball of lead 3cm in diameter is melted and recast into three spherical balls. If the diameters of two balls be $\frac{3}{2}$cm and 2cm,
find the diameter of the third ball.
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Q 254 Mark Question4 Marks
A hollow sphere of internal and external radii 2cm and 4cm respectively is melted into a cone of base radius 4cm.
Find the height and slant height of the cone.
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