Question

A cubical ice-cream brick of edge 22 cm is to be distributed among some children by filling ice-cream comes of radius 2 cm and height 7cm up to its brim. Take π = 3.14. 

(a) Surface area of ice-cream cube is: 

(i). \(2\sqrt{53}\)π cm² 

(ii). 2904 cm² 

(iii).22³ cm² 

(iv).None 

(b) Volume of ice-cream cube is:

(i). \(\frac{88}3\) cm³

(ii). 10512 cm³ 

(iii).22³ cm³ 

(iv).None.

(c) Volume of each cone is: 

(i). \(\frac{88}3\) cm³ 

(ii). 37 cm³ 

(iii).360 cm³ 

(iv).None. 

(d) The number of children who will get the ice-cream cones is: 

(i). 320 

(ii). 363 

(iii).350 

(iv).None. 

(e) Slant height of each cone is: 

(i). \(\sqrt{53}\) cm 

(ii). 7 cm 

(iii). 8 cm 

(iv). None.

Answer 1

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.