the total surface area of a right circular cone of slant height 13 cm is 90 pi cm square calculatenumber 1) its radius in centimetre 2) its volume in centimetre cube [take pie = 3.14]
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Answered by
114
heya mate !!
here's your answer :-
\_______________________/
Given that ,
● Total surface area of right circular cone = 90 π cm^2
● Slant height = 13 cm
So , Let's unlock the question :-
\_______________________/
☆ ques. 1 [ to find it's radius ]
□ Total surface area of right circular cone = π r ( l + r )
▪ On putting the values , we get :-
==> π r ( 13 + r ) = 90 π cm^2
==> r ( 13 + r ) = 90 cm^2 ( both sides r divided by π )
==> 13r + r^2 = 90
==> r^2 + 13r - 90 = 0
On solving , we get
==> r^2 + 18r - 5r - 90 = 0
Taking common :-
==> r ( r + 18 ) - 5 ( r + 18 )
==> ( r - 5 ) ( r + 18 )
==> ( r - 5 ) = 0 , ( r + 18 ) = 0
==> r = 5 and
==> r = -18 ( can not be negative )
__________________________
Hence , it's radius is 5 cm.
__________________________
ques. = 2 ( To find it's volume )
We have ,
● Radius = 5 cm
● Slant height , l = 13 cm
● height = ?
☆ h =√ l^2 - h^2
On putting values ,
==> h =√ 13^2 - 5^2
==> h = √ 169 - 25
==> h = √ 144
==> h = 12
________________________
Volume of the cone = 1 / 3 π r^2 h cm^3
==> 1 / 3 * 3.14 * 5^2 * 12
==> 1 / 3 * 3.14 * 25 * 12
==> 3.14 * 25 * 12 / 3
==> 3.14 * 25 * 4
==> 3.14 * 100
==> 314 cm^3.
________________________
hence , it's radius = 5 cm
And it's volume = 314 cm^3
________________________
hope it helps !!
thanks for asking :)
☆ be brainly ☆
here's your answer :-
\_______________________/
Given that ,
● Total surface area of right circular cone = 90 π cm^2
● Slant height = 13 cm
So , Let's unlock the question :-
\_______________________/
☆ ques. 1 [ to find it's radius ]
□ Total surface area of right circular cone = π r ( l + r )
▪ On putting the values , we get :-
==> π r ( 13 + r ) = 90 π cm^2
==> r ( 13 + r ) = 90 cm^2 ( both sides r divided by π )
==> 13r + r^2 = 90
==> r^2 + 13r - 90 = 0
On solving , we get
==> r^2 + 18r - 5r - 90 = 0
Taking common :-
==> r ( r + 18 ) - 5 ( r + 18 )
==> ( r - 5 ) ( r + 18 )
==> ( r - 5 ) = 0 , ( r + 18 ) = 0
==> r = 5 and
==> r = -18 ( can not be negative )
__________________________
Hence , it's radius is 5 cm.
__________________________
ques. = 2 ( To find it's volume )
We have ,
● Radius = 5 cm
● Slant height , l = 13 cm
● height = ?
☆ h =√ l^2 - h^2
On putting values ,
==> h =√ 13^2 - 5^2
==> h = √ 169 - 25
==> h = √ 144
==> h = 12
________________________
Volume of the cone = 1 / 3 π r^2 h cm^3
==> 1 / 3 * 3.14 * 5^2 * 12
==> 1 / 3 * 3.14 * 25 * 12
==> 3.14 * 25 * 12 / 3
==> 3.14 * 25 * 4
==> 3.14 * 100
==> 314 cm^3.
________________________
hence , it's radius = 5 cm
And it's volume = 314 cm^3
________________________
hope it helps !!
thanks for asking :)
☆ be brainly ☆
Answered by
45
Answer:
Radius = 5 cm
Volume = ≈ 314 cm^3
Step-by-step explanation:
Total surface area of right circular cone = r(l+r)
90 = r(13+r)
90/ = r(13+r)
90 = 13r+r^2
r^2 + 13r - 90 = 0
r^2 + 18r - 5r + 90 (By splitting the middle term)
r(r + 18) - 5(r+18) (By taking common)
(r-5)(r+18)
r = 5
r = -18 ( radius cannot be negative)
So, r = 5cm
l² = √h² + r²
13² = √h² + 5²
169 = √h² + 25
h = √169-25
h = √144
h = √12 cm
Volume of cone = 1/3h
= 1/3 * 3.14 * 5 * 5 * 12
= 314 cm^3
Hope it help. Please mark it as the brainliest.
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