1 The total surface area of a cube is 32 2/3m2 Find the volume of the cube - Maths - Surface Areas and Volumes

Question

1 The total surface area of a cube is 32
2/3  m 2 Find the
volume of the cube

2 The area of three adjacent
faces of a cuboid are p, q, and r If v its volume is v, prove that
v2=pqr
3 A cylindrical metallic pipe
is 21cm long The difference between the outside and inside surface
is 66cm2 If the pipe is made up of 148 5cm3
of metal, find the outer and inner radii of the pipe
4 1 cm3 of gold is
drawn to a wire 0 1mm in diameter Find the length of the wire

Ayush Jha · Accepted Answer

1> The total surface area of the cube is $32 \frac{2}{3} m^{2}$

Let the side of the cube be a.

Since,

$6 a^{2} = \frac{98}{3} a = \sqrt{\frac{98}{18}} a = 2.33 m$

Volume of the cube is-

$= a^{3} = {(2.33)}^{3} = 12.703 m^{3}$

2>We have the area of adjacent faces of a cuboid as p,q,r.

Let the sides of the adjacent sides of the cuboid be a,b,c.

Volume of the cuboid is given by abc.

Since,

$a b = p b c = q a c = r$

Multiply all the above three equations to get,

${(a b c)}^{2} = p q r V^{2} = p q r$

Hence proved.

3> Length of the cylindrical metallic pipe is 21 cm.

The volume of metal consumed in the formation of pipe is $148.5 {c m}^{3}$

The difference in the outer and the inner surface is 66 ${c m}^{2}$

Ler the inner radius be r and outer radius,R

Since,

$O u t e r S u r f a c e a r e a - I n n e r S u r f a c e a r e a = 66$

So,

$2 Π h (R - r) = 66 R - r = \frac{1}{2}$ ......(1)

Now,

$Π h (R^{2} - r^{2}) = 148.5 (R + r) (R - r) = \frac{148.5}{\frac{22}{7} (21)} R + r = 4.5$ .......(2)

Using equation (1) and (2),

$R = 2.5 c m r = 2 c m$

4> Length of the wire can be calculated as-

Let the length of the wire be h.

We have the volume of the gold= $1 {c m}^{3}$

$V o l u m e = Π {(\frac{d}{2})}^{2} h$

Hence,

$1 = \frac{22}{7} (\frac{0.01}{2}) h h = \frac{14}{0.22} = 63.63 c m$