A cubical ice-cream brick of edge 22 cm is to be distributed among som

1.	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» 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.

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»

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.

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