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Surface Area And Volume of Sphere MATHS - Surface Area And Volume of Sphere

UP Board (UPMSP) - STD 9 - MATHS (UPMSP - English Medium). 115 questions in this chapter.

Question types

Surface Area And Volume of Sphere question types

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

115
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 1M.C.Q1 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 2M.C.Q1 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 3M.C.Q1 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 4M.C.Q1 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 5M.C.Q1 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 Marks Questions2 Marks
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. $\Big(\text{Use }\pi=\frac{22}{7}\Big).$
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Q 142 Marks Questions2 Marks
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.
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Q 152 Marks Questions2 Marks
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?
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Q 163 Marks Question3 Marks
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.
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Q 193 Marks Question3 Marks
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 $100cm^2$
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Q 203 Marks Question3 Marks
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 $100cm^2$
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Q 214 Marks Questions4 Marks
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?
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Q 234 Marks Questions4 Marks
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 $100cm^2$
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Q 244 Marks Questions4 Marks
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.
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Q 254 Marks Questions4 Marks
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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