A semicircular sheet of metal of radius 14 cm is bent to form an open conical cup of the largest size. Find the capacity of the cup. (Take )

Question

KnowledgeBoat · Accepted Answer

Semicircular sheet of metal of radius 14 cm is shown in the figure below: On bending the semicircular sheet in the form of cone, Slant height of cone = Radius of sheet (r) = 14 cm Also, the circumference of base of cone = Circumference of semi-circular sheet. Let radius of cone be R cm and height be h cm. ⇒ 2πR = πr ⇒ r = 2R ⇒ R = = 7 cm. By formula, ⇒ (Slant height)2 = Height2 + Radius2 ⇒ l2 = h2 + R2 ⇒ 142 = h2 + 72 ⇒ 196 = h2 + 49 ⇒ h2 = 196 - 49 ⇒ h2 = 147 ⇒ h = = 12.124 cm Volume of cone = Hence, capacity of cup = 622.37 cm3.

Mid-value	Frequency
28	10
34	8
40	24
46	16
52	8

Mathematics

A semicircular sheet of metal of radius 14 cm is bent to form an open conical cup of the largest size. Find the capacity of the cup. (Take )

Mensuration

Related Questions

If the third, sixth and the last terms of a G.P. are 6, 48 and 3072 respectively, find the first term and the numbers of terms in the G.P.

Find the mode of the following distribution by drawing a histogram :
Mid-value Frequency
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P and Q are two points on the x-axis and y-axis respectively. M(3, 2) divides the line segment PQ in the ratio 2 : 3. Find :
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Mathematics

A semicircular sheet of metal of radius 14 cm is bent to form an open conical cup of the largest size. Find the capacity of the cup. (Take )

Mensuration

Related Questions

If the third, sixth and the last terms of a G.P. are 6, 48 and 3072 respectively, find the first term and the numbers of terms in the G.P.

Find the mode of the following distribution by drawing a histogram :Mid-valueFrequency281034840244616528

P and Q are two points on the x-axis and y-axis respectively. M(3, 2) divides the line segment PQ in the ratio 2 : 3. Find :(i) the co-ordinates of the points P and Q(ii) the slope of line segment PQ(iii) the equation of the line through point P and perpendicular to PQ.

Find the mode of the following distribution by drawing a histogram :
Mid-value Frequency
28 10
34 8
40 24
46 16
52 8

P and Q are two points on the x-axis and y-axis respectively. M(3, 2) divides the line segment PQ in the ratio 2 : 3. Find :
(i) the co-ordinates of the points P and Q
(ii) the slope of line segment PQ
(iii) the equation of the line through point P and perpendicular to PQ.