**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 cm^{3}**

**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 cm^{2}**

**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 cm^{2}**

**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 =

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

Therefore it’s diagonal, AD = cm

*Alternate method: *

Diagonal of a cube of 6 cm :

= 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 cm^{3}

**Hence, option c) is correct option.**

**3. Curved surface area of hemispherical ice-cream:**

The curved area of hemisphere =

Here, given that base radius, cm

curved area of hemispherical icecream =

= 2 x 22 x 7 = 308 cm^{2}

**Hence, option b) is correct option**

**4. Slant height of a cone:**

From the adjoining figure:

Given that the Radius of the cone, = 7 cm

Height of the cone, = 24 cm

Now, from the adjoining figure:

= 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, = 7 cm

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

Therefore, surface area of conical base =

= 22 x 25 = 550 cm^{2}

B) curved surface area of hemispherical icecream = 308 cm^{2} (calculated in part 3)

Therefore, Total surface area = 550 + 308 = 858 cm^{2}

**Hence, option a) is correct option.**

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