43957.What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?
344.35 $cm^2$
462 $cm^2$
498.35 $cm^2$
None of these
Explanation:
h = 14 cm, r = 7 cm.
So, l = $ \sqrt{(7)^2 + (14)^2} = \sqrt{245} = 7\sqrt{5} cm$
ஃ Total surface area = $\pi$ rl + $\pi r2$
= $(\dfrac{22}{7} \times 7 \times 7\sqrt{5} + \dfrac{22}{7} \times 7 \times 7 ) cm^2 $
= $[154(\sqrt{5} + 1)] cm^2 $
= (154 x 3.236) $cm^2$
= 498.35 $cm^2.$
h = 14 cm, r = 7 cm.
So, l = $ \sqrt{(7)^2 + (14)^2} = \sqrt{245} = 7\sqrt{5} cm$
ஃ Total surface area = $\pi$ rl + $\pi r2$
= $(\dfrac{22}{7} \times 7 \times 7\sqrt{5} + \dfrac{22}{7} \times 7 \times 7 ) cm^2 $
= $[154(\sqrt{5} + 1)] cm^2 $
= (154 x 3.236) $cm^2$
= 498.35 $cm^2.$
43958.A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:
$12 cm^3 $
$15 cm^3$
$16 cm^3$
$20 cm^3$
Explanation:
Clearly, we have r = 3 cm and h = 4 cm.
ஃ Volume = $\dfrac{1}{3} \pi r^2h = (\dfrac{1}{3} \times pi \times 3^2)cm^3$ = 12$\pi cm^3$.
Clearly, we have r = 3 cm and h = 4 cm.
ஃ Volume = $\dfrac{1}{3} \pi r^2h = (\dfrac{1}{3} \times pi \times 3^2)cm^3$ = 12$\pi cm^3$.
43964.A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?
2 : 1
3 : 2
25 : 18
27 : 20
Explanation:
Volume of the large cube = $(3^3 + 4^3 + 5^3) = 216 cm^3.$
Let the edge of the large cube be a.
So, $a^3 $= 216 a = 6 cm.
ஃ Required ratio = $(\dfrac{6 x (3^2 + 4^2 + 5^2)}{6 x 6^2}) = \dfrac{50}{36} $= 25 : 18
Volume of the large cube = $(3^3 + 4^3 + 5^3) = 216 cm^3.$
Let the edge of the large cube be a.
So, $a^3 $= 216 a = 6 cm.
ஃ Required ratio = $(\dfrac{6 x (3^2 + 4^2 + 5^2)}{6 x 6^2}) = \dfrac{50}{36} $= 25 : 18
43965.66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:
84
90
168
336
Explanation:
Let the length of the wire be h.
Radius = $\dfrac{1}{2}mm = \dfrac{1}{20}cm$. Then,
=> $\dfrac{22}{7} \times \dfrac{1}{20} \times \dfrac{1}{20} \times h = 66$
=> h =$ (\dfrac{66 \times 20 \times 20 \times 7}{22}) = 8400cm = 84 m$
Let the length of the wire be h.
Radius = $\dfrac{1}{2}mm = \dfrac{1}{20}cm$. Then,
=> $\dfrac{22}{7} \times \dfrac{1}{20} \times \dfrac{1}{20} \times h = 66$
=> h =$ (\dfrac{66 \times 20 \times 20 \times 7}{22}) = 8400cm = 84 m$
44166.Find the length of the longest pole that can be placed in a room 12m long 8m broad and 9m high.
12
13
15
17
Explanation:
Sol. Length of longest pole = Length of the diagonal of the room
= √(122+82+92= √(289)= 17 m.
Sol. Length of longest pole = Length of the diagonal of the room
= √(122+82+92= √(289)= 17 m.
44168.Find the volume and surface area of a cuboid 16 m long, 14 m broad and 7 m hight.
680
712
868
None of these
Explanation:
Volume = (16 $\times 14 \times 7) m^3 = 1568 m^3.$
Surface area = $[2 (16 x 14 + 14 \times 7 + 16 \times 7)] cm^2$
= (2 x 434)$ cm^2 = 868 cm^2.$
Volume = (16 $\times 14 \times 7) m^3 = 1568 m^3.$
Surface area = $[2 (16 x 14 + 14 \times 7 + 16 \times 7)] cm^2$
= (2 x 434)$ cm^2 = 868 cm^2.$
44169.Given a cylinder with the radius 5cm and height 8cm. Find the volume of this cylinder. Take π as 3.14.
251.2$ cm^2$
251.2 $cm^3$
628 $cm^2$
628 $cm^3$
Explanation:
volume of a cylinder = $πr^2ℎ$
= $3.142 \times 5 \times 5 \times 8$
= 628 $cm^3$
volume of a cylinder = $πr^2ℎ$
= $3.142 \times 5 \times 5 \times 8$
= 628 $cm^3$
44171.The perimeter of one face of a cube is 20 cm. Its volume will be:
125cm3
400cm3
250cm3
625cm3
Explanation:
Edge of cude = 20/4 = 5 cm
Volume = a*a*a = 5*5*5 = 125 cm cube
Edge of cude = 20/4 = 5 cm
Volume = a*a*a = 5*5*5 = 125 cm cube
44175.A spherical ball has a surface area of $\dfrac{792}{7}$sq. m. Find its volume.
7 sq.cm.
792/7 cu.cm.
792π/7 cu.cm.
792 cu.cm.
Explanation:
Surface area =$\dfrac{792}{7}$
∴$ r^2 = \dfrac{792 \times 7}{7 \times 4 \times 22}$
∴ r = 3cm
Volume = $\dfrac{4}{3} \pi r^3$ = $\dfrac{4}{3} \times 3.142 \times 3^3$
= 104 cu.cm.
Surface area =$\dfrac{792}{7}$
∴$ r^2 = \dfrac{792 \times 7}{7 \times 4 \times 22}$
∴ r = 3cm
Volume = $\dfrac{4}{3} \pi r^3$ = $\dfrac{4}{3} \times 3.142 \times 3^3$
= 104 cu.cm.
44178.When Jaya divided surface area of a sphere by the sphere’s volume, she got the answer as $\dfrac{1}{18}$ cm. What is the radius of the sphere?
24 cm
6 cm
54 cm
4.5 cm
Explanation:
$\dfrac{4 \pi r^2}{\dfrac{4}{3} \pi r^3}$ = $\dfrac{1}{18}$
∴ $\dfrac{3}{r}$ = $\dfrac{1}{18}$
∴ r=54 cm
$\dfrac{4 \pi r^2}{\dfrac{4}{3} \pi r^3}$ = $\dfrac{1}{18}$
∴ $\dfrac{3}{r}$ = $\dfrac{1}{18}$
∴ r=54 cm