# Free Surface Areas and Volumes 02 Practice Test - 9th Grade

### Question 1

The cost of painting the curved surface area of a cylindrical pillar of height 10 m and radius 3.5 m at ₹* *10/- per sq. meter is ₹* *2200/-.

(use π=227)

True

False

#### SOLUTION

Solution :A

Curved surface area of the cylindrical pillar

=2πrh

=2×227×3.5×10

=220 m2

So,

total cost of painting

=Curved Surface Area of pillar×Cost per m2

=220×10

= ₹ 2200/-

Hence, the given statement is true.

### Question 2

The radius of a hemisphere having total surface area of 1848 sq. cm is 7 cm.

True

False

#### SOLUTION

Solution :B

Total surface area =3πr2

⇒3×227×r2=1848

⇒r2=1848×73×22

⇒r2=196

⇒r=14 cm

Thus, above statement is false.

### Question 3

Meena needs to serve mango juice to her guests in cylindrical tumblers of radius 7 cm up to a height of 10 cm. If she wants to serve 25 guests, how much juice should she prepare?

35 L

42.5 L

38.5 L

50 L

#### SOLUTION

Solution :C

We know that,

Volume of a cylindrical container

=πr2h

1000 cm3=1 L

Hence, the volume of each cylindrical tumbler

=227×72×10

=1540 cm3So, the total volume of juice required

=1540×25

=38500 cm3

= 38.5 L

### Question 4

The ratio of the radius to the height of a right cone is 3:4. Then the ratio of total surface area to curved surface of the cone is____.

2:3

3:5

7:9

8:5

#### SOLUTION

Solution :D

Given that,

r:h = 3:4

Let r = 3x and h = 4xFrom the relation

l2=h2+r2,

The Slant height:

l=√(3x)2+(4x)2

⇒l=5x

We know that,

Total surface area of cone

=πr(r+l)

Curved surface area of cone

=πrlHence, the required ratio

=Total surface area of coneCurved surface area

=πr(r+l)πrl

=π×3x(3x+5x)π×3x×5x

=8:5

### Question 5

A conical dome of a palace is supported by a cylindrical pillar, both having the same radius. If the ratio of the height of the pillar to that of dome is 4:3, then what is the ratio of their volumes?

2:1

3:1

4:1

1:1

#### SOLUTION

Solution :C

Given that, the ratio of the height of the pillar to that of dome is 4:3 .

⇒hcylinderhcone=43

We know that,

volume of cylinder=πr2h.

volume of cone=13πr2h.

Now, ratio of volume of cylinder to the volume of cone

=πr2hcylinder13πr2hcone

=πr2×413πr2×3

=41

=4:1

### Question 6

The total surface area in m2 of a cuboid with dimensions of 26m, 14m and 6.5m respectively is

#### SOLUTION

Solution :Total Surface Area = 2( l x b + b x h + h x l)

= 2(26 x 14 + 14 x 6.5 + 6.5 x 26)

= 2(364 + 91 + 169

=1248 m2

### Question 7

There is a conical tent whose slant height is 14 m. If the curved surface area of cone is 308 m2,^{ }then its base area is _______.

132 m2

224 m2

254 m2

154 m2

#### SOLUTION

Solution :D

The curved surface area of a cone = πrl

where, r is radius and l is slant height.⇒308=πrl

⇒ 227×r×14=308

⇒r=308×722×14

⇒r=7 mBase area

=πr2

=227×72

=154 m2

### Question 8

The water in a cubical tank of side 10m is transferred to completely fill a cuboidal tank of length 5m and breadth 10 and height h. Then the height of the cuboidal tank (in metres) is

#### SOLUTION

Solution :Volume of cube = (side)3

Volume of cuboid = (length) × (breadth) × (height)

So height of cuboidal tank can be found by equating the two

∴height=side3length×breadth

=1035×10∴ Height = 20m

### Question 9

An iron spherical ball of radius 21cm is melted and it is re-casted in hemispheres of radius 7cm. The number of balls formed will be

#### SOLUTION

Solution :The volume will remain constant.

Let's assume x such hemispherical balls will be formed.

So 43πR3=x23πr3

(Where R is the radius of spherical ball and r is the radius of the hemispheres)

⇒43π(21)3=x23π(7)3⇒x=2×21×21×217×7×7

⇒x=54

### Question 10

The volume of a cylinder is 231 cm3 and its height is 6 cm. A ball will fit inside the cylinder if its radius is ______.

3 cm

4 cm

2.5 cm

5 cm

#### SOLUTION

Solution :A and C

Volume of cylinder =π×r2×h

⇒231=227×r2×6

⇒r2=231×722×16

⇒r2=12.25

⇒r=3.5

So, a ball will fit inside the cylinder if its radius is less than or equal to 3.5 cm.