The edge of cubical ice-cream brick is a =22 cm.
The radius and height of the ice-cream cone are 2cm and 7cm, respectively.
(a) Surface area of ice-cream cube = 6a2 = 6 × 222 = 6 × 484 = 2904 cm2 .
(∵ The surface area of the cube is 6a2 )
Hence, option (ii) is correct.
(b) The volume of ice-cream cube = a3 = 223 cm3 . (∵ The volume of the cube is a3)
Hence, option (iii) is correct.
(c) The volume of each cone = \(\frac{1}3πr^2h\) = \(\frac{1}3\) x \(\frac{22}7\) x 2 x 2 x 7 = \(\frac{22\times4}3\) = \(\frac{88}3\) cm3
∵ r = 2 cm, h = 7 cm & π = \(\frac{22}7\)
Hence, option (i) is correct.
(d) Let n number of children will get the ice-cream cones which are filled from cubical ice-brick.
∴ n × Volume of one cone = Volume of ice-cream cube
⇒ n × \(\frac{88}3\) = 223
(∵ the volume of ice– cream cube = 223 & the volume of one ice cone = \(\frac{88}3\) )
⇒ n = \(\frac{22\times22\times22\times3}{22\times4}\) = 11 × 11 × 3 = 363.
∴ Total ice-cones are 363.
Hence, option (ii) is correct.
(e) The slant height of the cone is l = \(\sqrt{r^2+h^2}\) = \(\sqrt{2^2+7^2}\) = \(\sqrt{4+49}\) = \(\sqrt{53}\) cm.
Hence, option (i) is correct.