Mensuration

Original volume of the cylinder = πr²h

New radius = 3r and new height = 3h

So, new volume = π(3r)²(3h) = 27πr²h

So, the volume will become 27 times of the original volume.

Area of the base = 1/2*(diagonal)²

1/2*6√2*6√2 = 36 m²

So, volume of the pyramid = 1/3*height*area of base

120 = 1/3*h*576

h = 10 m

Curved surface area of sphere/Curved surface area of cylinder = 2/7

4πr²/2πrh = 2/7

2r/h = 2/7

h = 49

Now, the ratio of radius and height of the cylinder = 7/49 = 1 : 7

As volume of the cylinder is equal to the volume of the sphere,

πr² × 12 = 4/3π9³

r² x 12 = (4 x 9 x 9 x 9)/3

r = 9 cm

The sector has taken out from a circle. Therefore, radii of both will be same. So, area of sector = (pie*r²*angle)/360 degree = 154/6 = (22*r²*60)/7*360 = 154/6 r = 7 cm Therefore, radius of circle = 7 cm.  

Side of square = 3 cm Area of square  = side x side                       = 3 x 3 =   9 cm2

Number of squares = 25Area covered by one square = 9 cm2  so Area of table top is 25 x 9 = 225 cm2

This is the right answer because the side of the square chart paper = 13 cm Area of the square chart paper = side * side                            = 13 cm * 13 cm = 169 sq. cm Radius of the colourful sticker = 7 cm Perimeter or circumference of the sticker = 2 * pi * radius                                             = 2 * 22/7 * 7 = 44 cm Perimeter or circumference of the sticker = 44 cm

Ans: 169 sq. cm; 44 cm

Diameter of old circle = 2 r Radius = r Area = pi * radius * radius Radius of new circle = 2 r Area of new circle = pi * 2 r * 2r                      => pi * 4 * radius * radius Ratio = area of old circle / area of new circle            => 1/4

Ans. 4 * pi * r * r ; 1/4

Given CSA cost = Rs. 92.40 at 2 paise/cm², CSA area = 9240/2 = 4620 cm². With radius r = 5h/3 (since 1 2/3 = 5/3), CSA = 2πrh = 2π(5h/3)h = (10π/3)h². Solving: h² = 4620 × 3/(10π) ≈ 441, so h ≈ 21 cm and r = 35 cm. Volume = πr²h = π(35)²(21) ≈ 80850 cm³. Option A is correct. Options B and C are digit permutations, D is incorrect.

Let l and w be the length and the width, respectively. lw = 120 And (l + 2)(w - 4) = 84 Substituting w = 120/l, we get (l + 2)(120 - 4l) = 84l Or l = 12 cm

Correct option is (4).

$\frac{d^2V}{dH^2}=\frac{1}{3}\pi[4-0]>0(Minima)\\ \text{So, for the largest volume of cone, the value of H should be 4/3}$

Volume of sphere = 4/3$\pi$r³ = 4/3$\pi$ (10.5)³ cm³ Volume of cone of base radius 3.5 cm and height 3 cm = 1/3$\pi$ (3.5)² x 3 cm³ Number of cones formed =$\frac{Volume of sphere}{Volume of cone} \Rightarrow \frac{4/3\pi \times 10.5 \times 10.5}{{1/3\pi}\times 3.5 \times 3.5 \times 3}$     $\Rightarrow$ 126