Question

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 19 cm and
the diameter of the cylinder is 7 cm. Then the volume and total surface area of the solid is
a) 641.3 cm
b) 684.84 cm
c) 682.82 cm
d) 685.83 cm
The answer should first digit with 6

Plz answer fast ✅✅
Total 35 points
plz answer​

Answer 1

Required Answer:-

a) 641.3 cm ✔

Explanation

Given:-

• The total height = 19 cm
• Diameter of Cylinder = Diameter of hemisphere = 7 cm

To Find:-

• Volume of Total surface area of solid.

Solution :-

Radius of Cylinder = Radius of hemisphere= 7/2 = 3.5cm

Height of 2 hemisphere = 2(7/2)cm = 7cm

Height of Cylinder solid,

= total height of solid - height of 2 hemisphere

= 19 - 7 cm

= 12cm

Volume of solid = πr^2h + 2 × 2/3πr^3

= πr^2h + 4/3πr^3

= πr^2( h + 4/3 × r)

= 22/7 × (7/2)^2 × (12 + 4/3 × 7/2)

= 77/2 (12 + 14/3)

= 77/2 × 50/3

= (77 × 25)/3

= 641.67cm^3 approx.

Therefore, volume of solid is 641.67cm^3.

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Total surface area = total surface area of cylinder + total surface area of two hemispheres

= 2πrh + 2(2πr^2)

= 2πrh + 4πr^2

= 2πr(h+2r)

= 2×(22/7)×7/2 (12 + 2 × 7/2)

= 22 × 19

= 418 cm^2

Therefore, the total surface area of the solid = 418cm^2.

Answer 2

Answer:

Answer

Let r cm be the radius and h cm the height of the cylinder. Then,

r=27​cm;h=(19−2×27​)cm=12cm

Also radius of hemisphere =27​cm=rcm

Now,

volume of the solid = volume of the cylinder + volume of two hemisphere

{πr2h+2(32​πr3)}cm3=πr2(h+34r​)cm3

=⎩⎪⎨⎪⎧​722​×(27​)2×(12+34​×27​)⎭⎪⎬⎪⎫​cm3=722​×27​×27​×350​cm3=641.66cm3

Surface area of the solid

=curved surface are of cylinder + surface area of two hemisphere

=(2πrh+2×2πr2)cm2

=2πr(h+2r)cm2

=2×722​×27​(12+2×722​×27​)cm2

=(2×722​×27​×19)cm2=418cm2

Step-by-step explanation: