the area of the base of a conical solid is 38.5 CM square and its volume is 154 centimetre cube find the Curved surface area of the solid
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Answered by
44
Heya !!!
Area of base of conical solid = 38.5 cm
πR² = 38.5
22/7 × R² = 38.5
R² = 38.5 × 7 /22
R² => 12.25 cm
R = ✓12.25 = 3.5 m
Volume of conical solid = 154
1/3 πR² H = 154
1/3 × 22/7 × 3.5 × 3.5 × H = 154
H = 154 × 21 / 22 × 3.5 × 3.5
H = 3234/269.5
H = 12 m
Slant height ( L ) = ✓ ( R)² + (H)²
=> ✓ ( 3.5)² + (12)²
=> ✓12.25 + 144
=> ✓ 156.25
=> 12.5 cm
Therefore,
CSA of solid = πRL
=> 22/7 × 3.5 × 12.5
=> 137.5 cm².
★ HOPE IT WILL HELP YOU ★
Area of base of conical solid = 38.5 cm
πR² = 38.5
22/7 × R² = 38.5
R² = 38.5 × 7 /22
R² => 12.25 cm
R = ✓12.25 = 3.5 m
Volume of conical solid = 154
1/3 πR² H = 154
1/3 × 22/7 × 3.5 × 3.5 × H = 154
H = 154 × 21 / 22 × 3.5 × 3.5
H = 3234/269.5
H = 12 m
Slant height ( L ) = ✓ ( R)² + (H)²
=> ✓ ( 3.5)² + (12)²
=> ✓12.25 + 144
=> ✓ 156.25
=> 12.5 cm
Therefore,
CSA of solid = πRL
=> 22/7 × 3.5 × 12.5
=> 137.5 cm².
★ HOPE IT WILL HELP YOU ★
shalorina:
tysm
Answered by
20
hii!!
here's Ur answer...
given the area of the base of the conical solid us given 38.5cm²
we know that the base of a cone is circular.
therefore πr² = 38.5cm²
==> 22/7 × r² = 38.5cm²
==> r² = 38.5/1 × 7/22
==> r² = 269.5/22
==> r² = 12.25
==> r = 3.5cm
hence, the radius of the base of the conical solid is 3.5cm.
volume of the conical solid = 154cm³
therefore 1/3πr²h = 154cm³
==> 1/3 × 22/7 × 3.5 × 3.5 × h = 154cm³
==> 22/6 × 3.5 × h = 154cm³
==> 77/6 × h = 154cm³
==> h = 154/1 × 6/77
==> h = 924/77
==> h = 12cm
now, we have to find the CSA (curved surface area) of the conical solid. and formula for finding it's CSA is πrl where length is the slant height.
so now we have to find it's slant height.
by Pythagoras thereom :-
l = slant height, r = radius and h = height
l² = r² + h²
l² = 3.5² + 12²
l² = 12.25 + 144
l² = 156.25
l = √156.25
l = 12.5cm
slant height of the conical solid is 12.5cm
CSA of the conical solid = πrl
= 22/7 × 3.5 × 12.5
= 962.5/7
= 137.5cm²
hope this helps..!!
here's Ur answer...
given the area of the base of the conical solid us given 38.5cm²
we know that the base of a cone is circular.
therefore πr² = 38.5cm²
==> 22/7 × r² = 38.5cm²
==> r² = 38.5/1 × 7/22
==> r² = 269.5/22
==> r² = 12.25
==> r = 3.5cm
hence, the radius of the base of the conical solid is 3.5cm.
volume of the conical solid = 154cm³
therefore 1/3πr²h = 154cm³
==> 1/3 × 22/7 × 3.5 × 3.5 × h = 154cm³
==> 22/6 × 3.5 × h = 154cm³
==> 77/6 × h = 154cm³
==> h = 154/1 × 6/77
==> h = 924/77
==> h = 12cm
now, we have to find the CSA (curved surface area) of the conical solid. and formula for finding it's CSA is πrl where length is the slant height.
so now we have to find it's slant height.
by Pythagoras thereom :-
l = slant height, r = radius and h = height
l² = r² + h²
l² = 3.5² + 12²
l² = 12.25 + 144
l² = 156.25
l = √156.25
l = 12.5cm
slant height of the conical solid is 12.5cm
CSA of the conical solid = πrl
= 22/7 × 3.5 × 12.5
= 962.5/7
= 137.5cm²
hope this helps..!!
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