Question

A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

Answer 1

(i) A cubical block of side 7 cm is surrounded by a hemisphere.
$\therefore$ Diameter of hemisphere is = 7 cm.
Radius of hemisphere, r = 3.5 cm
$\therefore$ Surface area of hemisphere = Curved surface area - Area of base of hemisphere
$=2\pi r^2-\pi r^2$
$=2\times \frac{22}{7}\times {\left(\frac{7}{2}\right)}^2-\frac{22}{7}\times {\left(\frac{7}{2}\right)}^2$
$=38.5$
(ii) The curved surface area of square,
$=6\times I^2$
$=6\times (7{)}^2$
$=6\times 49$
$=294$ sq.cm.
$\therefore$ Total surface area of cubical block = Curved surface area of cubical block + Surface area of hemisphere
= 294 + 38.5
= 332.5 sq.cm.