Question

There are many varieties of mushrooms available in the world. One such mushroom ‘Amanita muscaria’ has a upper part which is like red cap (hemispherical) and lower part is like white stem (cylinderical). The hemispherical cap’s radius = 3 cm and cylindrical stem is 2 cm high with diameter 1.4 cm.

Considering mushroom a solid object, answer the following questions:

(i) What is the total height of a mushroom?

(ii) Find the volume of the stem.

(iii) (a) Determine the volume of 7 such mushrooms.

OR

(b) Find the total surface area of 7 such mushrooms.

Answer 1

(i) Total height = Height of cylindrical part + Height of hemispherical part

= 2 cm + 3 cm

= 5 cm

(ii) Volume of stem = Volume of cylinder

= πr²h

= `22/7 xx 1.4/20 xx 14/20 xx 2`

= 3.08 cm³

(iii) (a) Volume of 7 such mushrooms

 = 7 × [Volume of hemisphere + Volume of cylinder]

= `7 xx [2/3 πR^3 + πr^2h]`

= `7 xx π [2/3 xx 3 xx 3 xx 3 + 1.4/20 xx 1.4/20 xx 2]`

= `7 xx 22/7 [18 + 0.98]`

=  18.98 × 22

=  417.56 cm³

OR

(b) Total surface area of 7 such mushrooms

 = 7 × [CSA of hemisphere + CSA of cylinder + Area of base + Area of ring]

= 7 [2πR² + 2πrh + πr² + πR² – πr²]

= 7π [2R² + 2rh + R²]

= `7 xx 22/7 [2 xx 3^2 + 2 xx 1.4/2 xx 2 + 3^2]`

 = 22 [29.8]

= 655.6 cm²