Question

The shape of a solid is like a right circular cylinder, both of which are straight semi spherical, the total height of the solid is 35 cm and the diameter of the cylinder is 1/4 of its height, find the volume and total surface area of ​​that solid
help me please ​

Answer 1

SOLUTION

GIVEN--

• Solid shape like circular right cylinder
• total height= 35 cm
• diameter is= 1/4 of its height

FIND

• area of the solid shape

NOW

Right circular cylinder both which are straight semicircle

Radius= d cm

Radius of every semicircle = d

___

2

height of cylinder = 4 d cm

total cylindrical height =

$(4d + \frac{d}{2} + \frac{d}{2} )$

cm = 5 d cm

because

5 d = 35 => d = 7

radius of semicircle=

$\frac{d}{2} = \frac{7}{2}$

height = ( 4 × 7 )

= 28 cm

Volume of solid shape = volume of cylinder + volume of two semicircle =

$(\pi \: r \: {}^{2} h \: + 2 \times \frac{2}{3} {\pi \: r}^{3} \\ \\ = \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times 28 + \frac{4}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times \frac{7}{2} cm \:$

= 1257.67 cm

HENCE ,, THE VOLUME IS 1257.67

Total area

LETS SEE FORMULA NOW -:

=( 2 πr h + 2 πr² + 2π² ) = 2πrh + 4 πr²

2 πr ( h + 2 r ) =

2 x 22 7

____. × __. × 28 + 7 cm

7 2

22 × 35

= 770 cm

THERE FORE TOTAL IS 770 CM