Free Surface Areas and Volumes 01 Practice Test - 9th Grade
Question 1
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)
192
202
198
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.
Question 2
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)
400 cm2
267 cm2
258 cm2
374 cm2
SOLUTION
Solution : D
Given,
Radius (r) = 7 cm
Slant height (l) = 10 cmArea 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.
Question 3
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)
516 m2
616 m2
586 m2
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.
Question 4
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 ____.
480
200
320
280
SOLUTION
Solution : C
1 litre = 1000 cm3
40 litres = 40000 cm3Volume of water in the container
=40 litres = 40000 cm3Volume 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
Question 5
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 ___________ .
0.25 cm2
1 cm2
3 cm2
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 cm2Now, 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.
Question 6
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)
₹ 220/-
₹ 110/-
₹ 170/-
₹ 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/−
Question 7
The volume of a cone of radius 7 cm and slant height 14 cm is ______.
(use π=227)
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=√142−72
h=√147=12.1243 cmVolume of a Cone
=13×π ×r2h
=13×227×72×12.1243
=622.381 cm3
Question 8
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______.
144 cm3
132 cm3
154 cm3
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
Question 9
Cuboids can be formed by stacking
Rectangles
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.
Question 10
Pavan drew a △ABC right angled at B. He says if the right angle triangle is rotated along AB then it will result in ___
Cone
Cube
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