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cbse 10th Standard Maths Surface Areas and Volumes Important Questions And Answers Study Material - QB365 Set C

Published on: 22/10/2025

Question Set C

cbse 10th Standard Maths Surface Areas and Volumes Important Questions And Answers Study Material - QB365

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Std: 10th Standard CBSE - Maths

chapter: Surface Areas and Volumes - Important Questions And Answers

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Questions:

Generic 2

10 x 2 = 20

A sphere of diameter 6 cm is dropped in a right circular cylindrical vessel partly filled with water. The diameter of the cylindrical vessel is 12 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the
cylindrical vessel?

A cylindrical glass tube with radius 10 cm has water up to a height of 9 cm. A metal cube of 8 cm edge is immersed completely. By how much the water level will rise in the glass tube?

The radius of a wire is decreased to one-third. If the volume is same, then find the length of the wire.

A 55 cm high cylindrical lamp-shade has small decorative mirrors on its either ends upto a width of 10 cm and 50 mm thick wire wound around all over to cover the middle part. How many revolutions will the wire take to cover it ?

If the radius of base of a cylinder is doubled and the height remains unchanged, then find the ratio of curved surface areas of new cylinder to old cylinder.

A rectangular piece of paper is 70 cm long and 20 cm wide. If a cylinder is formed by rolling the paper along its breadth, then find the height of the cylinder so formed.

A heap of rice is in the form of a cone of diameter 9 m and height 3.5 m. Find the volume of the rice. How much canvas cloth is required to just cover the heap ?

The slant height of a frustum of a cone is 10 cm. If the height of the frustum is 8 cm then find the difference of the radii of its two circular ends.

A fez, the cap used by the Turks, is shaped like the frustum of a cone (see figure). If its radius on the open side is 10 cm, radius at the upper base is 4 cm and its slant height is 15 cm, find the area of material used for making it.

10.

The base radii of two right circular cylinders of the same height are in the ratio 3 : 5 Find the ratio of their curved surface area.

Multiple Choice Question

10 x 1 = 10

11.

A surahi is the combination of

(a)

a sphere and a cylinder

(b)

a hemisphere and a cylinder

(c)

two hemispheres

(d)

a cylinder and a cone

12.

What is \(1-\sqrt { 3 } \)?

(a)

Non terminating repeating

(b)

Non terminating non repeating

(c)

Terminating

(d)

None of the above

13.

If the surface area of a sphere is 144 π cm2, then its radius is

(a)

8 cm

(b)

10 cm

(c)

12 cm

(d)

6 cm

14.

A circular tent is cylinder to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, then the area of canvas required is

(a)

1760 m²

(b)

3960 m²

(c)

7920 m²

(d)

2640 m²

15.

If H and h be the heights of two cylinders, then the ratio of curved surface areas of two cylinders with equal radii is

(a)

√H : 2√h

(b)

H : h

(c)

H² : h²

(d)

2H : h

16.

Total surface area of a cylinder is equal to

(a)

πr + 2πrh

(b)

2πrh

(c)

πr²h

(d)

2πr(h + r)

17.

If the radius of the base of a right circular cylinder is halved keeping the height same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

(a)

1:2

(b)

2:1

(c)

4:1

(d)

1:4

18.

If a right angled triangle is revolved about one of the sides containing the right angle it forms a

(a)

Right circular cone

(b)

Right triangle

(c)

Prism

(d)

Pyramid

19.

What is the area of a semi–circle of radius 5 cm?

(a)

78.57 cm

(b)

71.42 cm

(c)

63.18 cm

(d)

79.86 cm

20.

If a solid, cone of base radius ‘r’ and height ‘h’ is placed over a solid cylinder having same base radius ‘r’ and height – ‘h’ as that of the cone, then the curved surface area of the shape is \(\pi \left( \sqrt { { h }^{ 2 }+r^{ 2 } } \right) +2\pi rh\) Is it true?

(a)

(b)

Yes

(c)

May be

(d)

Cannot be determined

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Answers Key:

Generic 2

10 x 2 = 20

Let the water level raised in cylindrical vessel be h cm
Volume of Sphere = Volume of water displaced in cylinder
\(\frac {4}{3}\pi\)(3)3 = \(\pi\)(6)²h
\(\frac {4}{3}\) x 27 = 36h
36=36h
h=1 cm

Let the height of water raised measured
=h cm
\(\therefore\) Volume of water displaced in cylinder
= \(\pi\)(10)²h
Volume of cube = 8 x 8 x 8 cm²
\(\pi\)(10)²h= 8 x 8 x 8
\(h=\frac { 8\times 8\times 8\times 7 }{ 22\times 10\times 10 } \)
=1.629 cm.

9 times

2 : 1

70 cm

Radius of conical heap of rice (r) \(={{9}\over{2}}=4.5\) m
Height of conical heap of rice (h) = .3.5 m
\(\therefore\) Volume of the rice \(={{1}\over{3}}\times{\pi}\times{r}^{2}\times h\)
\(={{1}\over{3}}\times{{22}\over{7}}\times4.5\times4.5\times3.5\)
= 74.25 m3
\(\therefore\) Slant height of the heap = \(\sqrt{(4.5)^{2}+(3.5)^{2}}\)
\(=\sqrt{20.25+12.25}\)
\(=\sqrt{}32.5\) = 5.7 m
Area of the canvas cloth = \({{22}\over{7}}\times4.5\times5.7\)
= 80.61 m²

\(\sqrt{h^{2}+\left(r_{2}-r_{1}\right)^{2}}\)=l
⇒ \(\sqrt{64+\left(r_{2}-r_{1}\right)^{2}}\)=10
⇒ (r₂-r₁)²=100-64
⇒ (r₂-r₁)²=36
⇒ r₂-r₁=6 cm

Radius (r₂) at upper circular end = 4 cm
Radius (r₁) at lower circular end = 10 cm
Slant height (l) of frustum = 15 cm
Area of material used for making the fez = CSA of frustum + Area of upper circular end
\(=\pi\left(r_{1}+r_{2}\right) l+\pi r_{2}^{2}\)
= π (10 + 4) 15 + π (4)²
= π (14) 15 + 16 π
\(\begin{array}{l} =210 \pi+16 \pi=\frac{226 \times 22}{7} \\ =710 \frac{2}{7} \mathrm{~cm}^{2} \end{array}\)
Therefore, the area of material used for making it is \(710 \frac{2}{7} \mathrm{~cm}^{2}\)

10.

Let radii of the cylinders be r₁=3x and r₂=5x, height=h
\(\frac { curved\quad surface\quad area\quad of\quad cylinder\quad I }{ curved\quad surface\quad area\quad of\quad cylinder\quad II } \)
=\(\frac{2\pi r_{1}h}{2\pi r_{2}h}\)=\(\frac{2\pi{\times}{3x}{\times}{h}}{2\pi{\times}{5x}{\times}{h}}\)=\(\frac{3}{5}\)
Required ratio=3:5

Multiple Choice Question

10 x 1 = 10

11.