# Free Surface Areas and Volumes 01 Practice Test - 9th Grade

A big iron boiler tank which is cylindrical in shape is open at the top. Its height is 10 m and radius is 7 m. It gets corroded at a rate of 3 m2/day. The number of days it will take to corrode completely is ____ .
(use π=227)

A.

192

B.

202

C.

198

D.

208

#### SOLUTION

Solution : C

Surface area of the boiler = Curved surface area of boiler + Base area of boiler
=2πrh+πr2
=2×227×7×10+227×72
=440+154
=594 m2

Now, number of days to corrode
=Total Surface Area of tankArea corroded per day
=5943
=198 days

Boiler will take 198 days to get corroded completely.

Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone should be 10 cm and 7 cm respectively. The area of the aluminium sheet required to make the cone is_____.
(Use π=227)

A.

400 cm2

B.

267 cm2

C.

258 cm2

D.

374 cm2

#### SOLUTION

Solution : D

Given,
Radius (r) = 7 cm
Slant height (l) = 10 cm

Area of the aluminium sheet required
=Total surface area of the cone
= πr(l+r)
= 227×7(10+7)
= 374 cm2

Hence, the area of the aluminium sheet required is 374 cm2.

In a circus, a motorcyclist performs his stunts inside a hollow sphere. The thickness of the sphere is negligible. If the diameter of the hollow sphere is 14 m, then find the area available for the motorcyclist to perform his stunts.
(use π=227)

A.

516 m2

B.

616 m2

C.

586 m2

D.

486 m2

#### SOLUTION

Solution : B

Radius of the sphere
=diameter2=142=7 m

Area available to the motorcyclist = Surface area of the sphere
=4πr2
=4×227×72

=616 m2

Hence, the available area to the motorcyclist is 616 m2.

A water container can hold 40 litres of water. Then the total number of ice cubes of side 5 cm which  the container can hold is ____.

A.

480

B.

200

C.

320

D.

280

#### SOLUTION

Solution : C

1 litre = 1000 cm3
40 litres = 40000 cm3

Volume of water in the container
=40 litres = 40000 cm3

Volume of each ice cube
=(Side)3
=53
=125 cm3

Number of ice cubes that can be fitted

=Volume of water containerVolume of each cube

=40000 cm3125 cm3

=320 ice cubes

A 3×3 Rubik's cube has a total surface area of 54 cm2. The area occupied by every single red tile of the cube is ___________ .

A.

0.25 cm2

B.

1 cm2

C.

3 cm2

D.

9 cm2

#### SOLUTION

Solution : B

Given,
Total surface area of the cube =54 cm2

We know that,
Cube has 6 number of faces.
Each face of the Rubik's cube contains 9 tiles.
Each Rubik's cube contains 9 red tiles.

Area of each face
=Total surface area of the cubeTotal number of faces of the cube=546=9 cm2

Now, area of each tile
=Area of each faceTotal number of  tiles in each face=99=1 cm2

Hence, the area occupied by every single red tile of the cube is 1 cm2.

A juice seller fills juice into cylindrical glasses from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges ₹10/- for a glass of height 10 cm and radius 4 cm. The amount he earns by selling the juice is ____.
(Use π=227)

A.

₹ 220/-

B.

₹ 110/-

C.

₹ 170/-

D.

₹ 190/-

#### SOLUTION

Solution : A

We know that,
volume of a cylinder =πr2h

Number of glasses of juice that are sold
=volume of the vesselvolume of each glass=π×10×10×35.2π×4×4×10=22

The amount earned by the shopkeeper
=Rate of each glass×Total number of glasses
=10×22= 220/

The volume of a cone of radius 7 cm and slant height 14 cm is ______.
(use π=227)

A. 622.381 cm3
B. 722.381 cm3
C. 618.381 cm3
D. 522.381 cm3

#### SOLUTION

Solution : A

Given,
Radius of the cone
r=7 cm
Slant height of the cone
l=14 cm From the pythagoras theorem
l2=h2 + r2,

height of the cone
h=14272
h=147=12.1243 cm

Volume of a Cone
=13×π ×r2h

=13×227×72×12.1243

=622.381 cm3

A hemispherical bowl fits exactly on the flat surface of a right circular cone whose height is 5 cm and radius is 3.5 cm. The volume of the solid formed is______. A.

144 cm3

B.

132 cm3

C.

154 cm3

D.

169 cm3

#### SOLUTION

Solution : C

We know that,
volume of cone =13πr2h
volume of hemisphere =23πr3

Total volume
= Volume of the cone + Volume of              the hemisphere

=13πr2h+23πr3=13πr2(h+2r)=13×227×3.52×(5+7)=13×227×3.52×12=22×0.5×3.5×4=154 cm3

The volume of the solid formed is
154 cm3

Cuboids can be formed by stacking

A.

Rectangles

B. Squares
C. Triangles
D. Trapezium

#### SOLUTION

Solution : A and B

Cuboids can be formed by stacking rectangles as shown in the figure. A   square can be defined as a rectangle in which the adjacent sides are equal. Thus, stacking squares also yields cuboids. In fact, we obtain a special type of cuboid in this case, called the cube.

Pavan drew a ABC right angled at B. He says if the right angle triangle is rotated along AB then it will result in ___

A.

Cone

B.

Cube

C. Cylinder
D. Cuboid

#### SOLUTION

Solution : A

If right angle triangle is rotated along any of it's perpendicular side then we will get a right circular cone. See the image below 