Test Level 1: Mensuration - 1 - CAT MCQ

Curved surface area of a cylinder = 2πrh
Given: h = 14 cm and curved surface area = 264 cm²
∴ 2πrh = 264
r = 3 cm

Here, 'l' is slant height,

As both have the same radius, therefore: 


Squaring both sides:

h/r = 3/1

According to the question, rotating square along a diagonal makes two right-circular cones.
As the diagonal makes a right-angled triangle by the sides of square, so
D = 9√2 m (Using Pythagoras theorem)

So, curved surface area of the cone = 2 πrl

According to the question:
Volume of the drum = πr²h

Volume of small can

Divide both the above volumes to get the maximum number of cans as 52.73, i.e. maximum 52 cans can be completely filled. 

Semi-perimeter (2a) = 18 cm
Area (a × a) = 81 cm²
Solving both, we get a = 9 cm.
Now, circumference = 2 × 18 = 36
So, r = 
Area of circle = 

Volume of water displaced by 150 men = 150 × 8 = 1200 m3
Let the rise in water level be x.
90 × 40 × x = 1200
⇒ x = 12/36 = 1/3 or 0.33 m = 33.33 cm (Approx.)

Radius of the sphere = 6/2 = 3 cm
Radius of the cylinder = 12/2 = 6cm
Volume of the sphere 

New volume of the cylindrical vessel - Initial volume of the cylindrical vessel = Volume of the sphere
Initial height = h cm
Final height = H cm
πr²H - πr²h = 36π

Since three metal cubes of volumes 125 cm³, 64 cm³ and 27 cm³ are melted to form a new cube,
Therefore, volume of the new cube = 125 + 64 + 27 = 216 cm³
Total volume = 216 cm³
a³ = 216 cm³
a³ = 6³
On comparing, we get
a = 6
Edge = 6 cm

Let each side of the cube be x cm.
Therefore, surface area = 6x²
Surface area of the cube after making the side of cube double = 6(2x)² = 24x²
So, clearly, it becomes 4 times of the previous one.
Percentage increase 

Height of the cylinder = 15 m
Height of the cone, 'h' = 19 - 15 = 4 m
Radius =  6/2 = 3 m
Slant height of the cone = 
Canvas required = C.S.A. of (cone + cylinder)
= πrl + 2πrH
= πr(5 + 2 × 15)

= 330 m²