Question

(1) If the volume of the earth dug out from a cubical pil is 4200 cubic cm, then
what is the measure of its edges?
(2) How many cubical cakes of edge 8 cm can be cut from a cake measuring
0.72 m by 0.19 m by 18 cm?​

Answer 1

Q.1

Given data : The volume of the earth dug out from a cubical pil is 4200 cubic cm.

To find : what is the measure of its edges ?

Solution : we know that all edges of cube are equal.

Here we use formula of volume of cube,

Now according to given,

⟹ volume of earth dug = volume of cube

⟹ volume of earth dug = (edge)³

⟹ 4200 = (edge)³

⟹ edge = ³√4200

⟹ edge = 16.13428646 cm

Answer : Hence, the edges of earth dug are 16.12428646 cm.

Q.2 :

Given data : How many cubical cakes of edge 8 cm can be cut from a cake measuring 0.72 m × 0.19 m × 18 cm ?

Solution : Here we know that,

⟹ 18 cm = 18/100 m

⟹ 18 cm = 0.18 m

Let, length of cake be 0.72 m and breadth of cake be 0.19 m and height of cake be 0.18 m.

Let, shape of cake be cuboidal.

⟹ volume of cuboidal cake

= length * breadth * height

⟹ volume of cuboidal cake

= 0.72 * 0.19 * 0.18

⟹ volume of cuboidal cake

= 0.0323 * 0.18

⟹ volume of cuboidal cake

= 0.005814 m³

Now,

⟹ 8 cm = 8/100 m

⟹ 8 cm = 0.08 m

Now according to given

⟹ volume of cubical cake = (edge)³

⟹ volume of cubical cake = (0.08)³

⟹ volume of cubical cake = 0.000512 m³

Now,

⟹ number of cubical cake

= {volume of cuboidal cake}/{volume of cubical cake}

⟹ number of cubical cake

= 0.005814/0.000512

⟹ number of cubical cake

= 2907/256

⟹ number of cubical cake

= 11.35546875

Answer : Hence, approximately 11 cubical cakes of edge 8 cm can be cut from a cake measuring 0.72 m × 0.19 m × 18 cm.