On a Sunday, your Parents took you to a fair

Q: On a Sunday, your Parents took you to a fair. You could see lot of toys displayed, and you wanted them to buy a RUBIK’s cube and strawberry ice-cream for you. Observe the figures and answer the questions:-

1. The length of the diagonal if each edge measures 6cm is

a) 3√3. b) 3√6. c) √12. d) 6√3

2. Volume of the solid figure if the length of the edge is 7cm is

a)256 cm^3.b) 196 cm^3.c) 343 cm^3.d) 434 cm³

3. What is the curved surface area of hemisphere (ice cream) if the base radius is 7cm?

a) 309 cm^2.b) 308 cm^2.c) 803 cm^2.d) 903 cm²

4. Slant height of a cone if the radius is 7cm and the height is 24 cm___

a) 26cm. b) 25 cm. c) 52 cm. d) 62cm

5. The total surface area of cone with hemispherical ice cream is

a) 858 cm^2.b) 885 cm^2.c) 588 cm^2.d) 855 cm²

Ans:

1. Diagonal of the cube:

Let’s look the entire diagonal as combination of two right angled triangles.

In 1st right angled triangle, ABC, base BC and height AB are 6 cm each,

Therefore it’s diagonal, AC = $\sqrt{6^2 + 6^2} = 6\sqrt2$

Now, In the 2nd right angled triangle ACD, base AC is $6\sqrt2$ cm and height CD is 6 cm.

Therefore it’s diagonal, AD = $\sqrt{6^2 + (6\sqrt2)^2} = 6\sqrt3$ cm

Alternate method:

Diagonal of a cube of 6 cm : $\sqrt {6^2 +6^2+6^2}$

= $6\sqrt3$ cm

Hence, option d) is correct option.

2. Volume of 7 cm cube:

Here solid figure is cube hence we will take cube as the solid figure.

Now, Volume of a cube is given by: (side)³

It is given that the length of the edge is 7cm,

Hence, volume of the cube = (7)3 = 343 cm³

Hence, option c) is correct option.

3. Curved surface area of hemispherical ice-cream:

The curved area of hemisphere = $2\pi r^2$

Here, given that base radius, $R_h_e_m = 7$ cm

curved area of hemispherical icecream = $2 (\frac{22}{7}) (7)^2$

= 2 x 22 x 7 = 308 cm²

Hence, option b) is correct option

4. Slant height of a cone:

From the adjoining figure:

$(R_c_o_n)^2 + (H_c_o_n)^2 = (L_c_o_n)^2$

Given that the Radius of the cone, $R_c_o_n$ = 7 cm

Height of the cone, $H_c_o_n$ = 24 cm

Now, from the adjoining figure:

$(L_c_o_n)^2 = (7)^2 + (24)^2 = 49 + 576 = 625 = (25)^2$

$L_c_o_n$ = 25 cm

Therefore, slant height of the cone is 25 cm.

Hence, option b) is correct option.

5. Total surface area of cone with hemispherical ice cream:

Total surface area = curved surface area of conical base + curved surface area of hemispherical icecream

A) Surface area of conical base = π r l

Here, radius of cone, $R_c_o_n$ = 7 cm

Slant height of cone, $L_c_o_n$ = 25 cm (calculated in part 4)

Therefore, surface area of conical base = $\frac {22}{7} \times (7) \times (25)$

= 22 x 25 = 550 cm²

B) curved surface area of hemispherical icecream = 308 cm² (calculated in part 3)

Therefore, Total surface area = 550 + 308 = 858 cm²

Hence, option a) is correct option.

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