Surface Areas and Volumes - CBSE STD 10 Maths Questions

Q 1M.C.Q (1 Marks)1 Mark

Choose the correct answer from the given four options:
A medicine$-$capsule is in the shape of a cylinder of diameter $0.5\ cm$ with two hemispheres stuck to each of its ends. The length of entire capsule is $2\ cm$. The capacity of the capsule is:

✓
$0.36 \ cm^3$
B
$0.35 \ cm^3$
C
$0.34 \ cm^3$
D
$0.33 \ cm^3$

Answer: A.

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Q 2M.C.Q (1 Marks)1 Mark

Choose the correct answer from the given four options:
A mason constructs a wall of dimensions $270\ cm \times 300\ cm \times 350\ cm$ with the bricks each of size $22.5\ cm \times 11.25\ cm \times 8.75\ cm$ and it is assumed that $\frac{1}{8}$ space is covered by the mortar. Then the number of bricks used to construct the wall is:

A
$11100$
✓
$11200$
C
$11000$
D
$11300$

Answer: B.

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Q 3M.C.Q (1 Marks)1 Mark

Choose the correct answer from the given four options:
The shape of a gilli, in the gilli-danda game see Fig. is a combination of:

A
Two cylinders.
B
A cone and a cylinder.
✓
Two cones and a cylinder.
D
Two cylinders and a cone.

Answer: C.

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Q 4M.C.Q (1 Marks)1 Mark

Choose the correct answer from the given four options:
A surahi is the combination of:

✓
A sphere and a cylinder.
B
A hemisphere and a cylinder.
C
Two hemispheres.
D
A cylinder and a cone.

Answer: A.

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Q 5M.C.Q (1 Marks)1 Mark

Choose the correct answer from the given four options:
The radii of the top and bottom of a bucket of slant height $45\ cm$ are $28\ cm$ and $7\ cm$, respectively. The curved surface area of the bucket is:

✓
$4950 \ cm^2$
B
$4951 \ cm^2$
C
$4952 \ cm^2$
D
$4953 \ cm^2$

Answer: A.

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Q 6True False[1 Marks ]1 Mark

Write ‘True’ or ‘False’ and justify your answer in the following:
A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is $4\pi\text{r h}+4\pi\text{r}^2.$

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Q 7True False[1 Marks ]1 Mark

Write ‘True’ or ‘False’ and justify your answer in the following: A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid $\pi\text{r}\Big[\sqrt{\text{r}^2+\text{h}^2}+3\text{r}+2\text{h}\Big].$

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Q 8True False[1 Marks ]1 Mark

Write ‘True’ or ‘False’ and justify your answer in the following: The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the Fig. is $\frac{\text{r}^2}{3}3\text{h}-2\text{r}.$

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Q 9True False[1 Marks ]1 Mark

Write ‘True’ or ‘False’ and justify your answer in the following:
A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is $\frac{4}{3}\pi\text{a}^3.$

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Q 10True False[1 Marks ]1 Mark

Write ‘True’ or ‘False’ and justify your answer in the following:
The curved surface area of a frustum of a cone is $\pi\text{l}(\text{r}_1+\text{r}_2),$ where $\text{l}\sqrt{\text{h}^2(\text{r}_1\ \ \text{r}_2)^2},$ $r_1$ and $r_2$ are the radii of the two ends of the frustum and h is the vertical height.

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Q 113 Marks Question3 Marks

Three metallic solid cubes whose edges are $3cm, 4cm$ and 5cm are melted and formed into a single cube. Find the edge of the cube so formed.

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Q 123 Marks Question3 Marks

How many shots each having diameter 3cm can be made from a cuboidal lead solid of dimensions $9cm × 11cm × 12cm?$

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Q 133 Marks Question3 Marks

A solid metallic hemisphere of radius 8cm is melted and recasted into a right circular cone of base radius 6cm. Determine the height of the cone.

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Q 143 Marks Question3 Marks

$500$ persons are taking a dip into a cuboidal pond which is $80m$ long and 50m broad. What is the rise of water level in the pond, if the average displacement of the water by a person is $0.04m^3$?

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Q 153 Marks Question3 Marks

A hemispherical bowl of internal radius 9cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5cm and height 4cm. How many bottles are needed to empty the bowl?

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Q 165 Marks Questions5 Marks

Water flows at the rate of 10m/ minute through a cylindrical pipe 5mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40cm and depth 24cm?

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Q 175 Marks Questions5 Marks

A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 6cm and 12cm, respectively. If the the slant height of the conical portion is 5cm, find the total surface area and volume of the rocket $[\text{Use }\pi=3.14].$

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Q 185 Marks Questions5 Marks

The barrel of a fountain pen, cylindrical in shape, is 7cm long and 5mm in diameter. A full barrel of ink in the pen is used up on writing 3300 words on an average. How many words can be written in a bottle of ink containing one fifth of a litre?

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Q 195 Marks Questions5 Marks

A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains $41\frac{19}{21}\text{m}^3$ of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building?

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Q 205 Marks Questions5 Marks

Find the number of metallic circular disc with 1.5cm base diameter and of height 0.2cm to be melted to form a right circular cylinder of height 10cm and diameter 4.5cm.

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Surface Areas and Volumes question types

Surface Areas and Volumes questions

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Surface Areas and Volumes Maths - Surface Areas and Volumes

Surface Areas and Volumes question types

Surface Areas and Volumes questions

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