Diameter of cylindrical tank = 2.8 m radius = 1.4 m Height = 4.2 m \[\begin{array}{*{35}{l}} Volume\text{ }of\text{ }water\text{ }filled\text{ }in\text{ }it\text{ }=\text{ }\pi {{r}^{2}}h \\...
FIGURE: Side of square (a) = 7m the radius of semi-circle = 7/2 m Length of the tunnel = 80 m \[\begin{array}{*{35}{l}} Area\text{ }of\text{ }cross\text{ }section\text{ }of\text{ }the\text{...
FIGURE: Side of square (a) = 7m the radius of semi-circle = 7/2 m Length of the tunnel = 80 m \[\begin{array}{*{35}{l}} Area\text{ }of\text{ }cross\text{ }section\text{ }of\text{ }the\text{...
Length of the platform = 22 m Circumference of semi-circle (c) = 11 m \[\begin{array}{*{35}{l}} radius\text{ }=\text{ }\left( c\text{ x }2 \right)/\text{ }\left( 2\text{ x }\pi \right)\text{...
Radius of the base of poles (r) = 6 cm Height of the cylindrical part (h1) = 110 cm Height of the conical part (h2) = 9 cm \[\begin{array}{*{35}{l}} Total\text{ }volume\text{ }of\text{ }the\text{...
Let edge of the cube = a Then, volume of the cube = a x a x a = a3 The sphere that exactly fits in the cube will have radius ‘a/2’ \[\begin{array}{*{35}{l}} Volume\text{ }of\text{ }sphere\text{...
Diameter of the sphere = 6 cm Radius = 3 cm \[~volume\text{ }=\text{ }4/3\text{ }\pi {{r}^{3~}}=\text{ }4/3\text{ x }22/7\text{ x }3\text{ x }3\text{ x }3\text{ }=\text{ }792/7\text{...
Radius of both cone and hemisphere = 8 cm And, height = 8 cm \[\begin{array}{*{35}{l}} Volume\text{ }of\text{ }the\text{ }solid\text{ }=\text{ }Volume\text{ }of\text{ }cone\text{ }+\text{...
Diameter of the cylinder = 12 cm => radius = 6 cm Height of the cylinder = 15 cm Diameter of the cone = 6 cm =>radius = 3 cm Height of the cone = 12 cm Radius of the hemisphere = 3 cm Let the...
Radius of the largest sphere that can be formed inside the cylinder will be equal to the radius of the cylinder. radius of the largest sphere = 7 cm \[\begin{array}{*{35}{l}} Volume\text{ }of\text{...
Diameter of solid metallic sphere = 6 cm So, its radius = 3 cm Height of solid metal cone = 45 Diameter of metal cone = 12 cm Its radius = 6 cm Let the number of solid metallic spheres be ‘n’...
Height of the cone (h) = 24 cm Height of the cylinder (H) = 36 cm Radius of the cone (r) = twice the radius of the cylinder = 10 cm Radius of the cylinder (R) = 5 cm \[\begin{array}{*{35}{l}}...
Diameter of the base = 3.5 m So, its radius = 3.5/2 m = 1.75 m = 7/4 m Height of cylindrical part = 4 + 2/3 = 14/3 (i) \[\begin{array}{*{35}{l}} Capacity\text{ }\left( volume \right)\text{ }of\text{...
Diameter of cylindrical boiler = 3.5 m So, the radius (r) = 3.5/2 = 35/20 = 7/4 m Height (h) = 2m Radius of hemisphere (R) = 7/4 m \[\begin{array}{*{35}{l}} Total\text{ }volume\text{ }of\text{...
Height of the cylindrical part = H = 8 m Height of the conical part = h = (13 – 8) m = 5 m Diameter = 24 m Its radius \[\begin{array}{*{35}{l}} =\text{ }24/2\text{ }=\text{ }12\text{ }m \\...
Radius of the cylindrical part of the tent (r) =105/2 m Slant height (l) = 80 m the total curved surface area of the tent \[\begin{array}{*{35}{l}} =\text{ }2\pi r\text{ }h\text{ }+\text{ }\pi rl ...
Radius of solid cylinder (R) = 12 cm And, Height (H) = 16 cm \[\begin{array}{*{35}{l}} Volume\text{ }=\text{ }\pi {{R}^{2~}}h\text{ }=\text{ }22/7\text{ }x\text{ }12\text{ }x\text{ }12\text{...
Height of the cylinder (h) = 10 cm And radius of the base (r) = 6 cm Volume of the cylinder = πr2 h Height of the cone = 10 cm Radius of the base of cone = 6 cm \[\begin{array}{*{35}{l}}...
Height of cone = 8 cm Radius = 5 cm \[\begin{array}{*{35}{l}} Volume\text{ }=~1/3\text{ }\pi {{r}^{2~}}h \\ =\text{ }1/3\text{ x }22/7\text{ x }5\text{ x }5\text{ x }8\text{ }c{{m}^{3}} \\ =\text{...
Since, the diameter of the largest hemisphere that can be placed on a face of a cube of side 7 cm will be 7 cm. radius = r = 7/2 cm It’s curved surface area = 2 πr2 = 2 x 22/7 x 7/2 x 7/2 = 77...
\[\left( iii \right)\text{ }Weight\text{ }of\text{ }material\text{ }drilled\text{ }out\text{ }=\text{ }1232\text{ x }7g\text{ }=\text{ }8624g\text{ }=\text{ }8.624\text{ }kg\]
Dimensions of rectangular solid l = 42 cm, b = 30 cm and h = 20 cm Conical cavity’s diameter = 14 cm its radius = 7 cm Depth (height) = 24 cm (i) Total surface area of cuboid...
Radius of the hemisphere part (r) = 3.5 m = 7/2 m Volume of hemisphere \[\begin{array}{*{35}{l}} =\text{ }2/3\text{ }\pi {{r}^{3}} \\ =\text{ }2/3\text{ x }22/7\text{ x }7/2x\text{ }7/2\text{ x...
Height of the cone = 15 cm Diameter of the cone = 7 cm its radius = 3.5 cm Radius of the hemisphere = 3.5 cm Volume of the solid = Volume of the cone + Volume of the hemisphere...
Radius of hemispherical bowl = 9 cm \[Volume\text{ }=\text{ }2/3\text{ }\pi {{r}^{3}}~=\text{ }2/3\text{ }\pi {{9}^{3}}~=\text{ }2/3\text{ }\pi \text{ }x\text{ }729\text{ }=\text{ }486\text{ }\pi...
Volume of rectangular block \[=\text{ }49\text{ x }44\text{ x }18\text{ }c{{m}^{3}}~=\text{ }38808\text{ }c{{m}^{3}}~\ldots \ldots \text{ }\left( i \right)\] Let r be the radius of sphere....
Let the radius of the smaller cone be r cm Diameter of bigger cone = 40 cm the radius = 20 cm and height = 9 cm \[\begin{array}{*{35}{l}} Volume\text{ }of\text{ }larger\text{ }cone\text{ }=\text{...
Height of the solid right circular cone = 32 cm Internal radius metallic spherical shell = 3 cm External radius spherical shell = 5 cm the volume of the spherical shell \[\begin{array}{*{35}{l}}...
External diameter of the hollow sphere = 8 cm radius (R) = 4 cm Internal diameter of the hollow sphere = 4 cm radius (r) = 2 cm Then, the volume of metal used in hollow sphere = Also given, Diameter...
Radius of the sphere = R = 15 cm So, the volume of sphere melted \[=\text{ }4/3\text{ }\pi {{R}^{2}}~=\text{ }4/3\text{ x }\pi \text{ x }15\text{ x }15\text{ x }15\] Radius of each cone recasted = r...
The volume of first sphere = 27 x volume of second sphere Let the radius of the first sphere = r1 and, radius of second sphere = r2 (i) Then, according to the question we have...
Radius of metallic sphere = 2mm = 1/5 cm \[\begin{array}{*{35}{l}} Volume\text{ }=\text{ }4/3\text{ }\pi {{r}^{3}}~=\text{ }4/3\text{ x }22/7\text{ x }1/5\text{ x }1/5\text{ x }1/5\text{ }=\text{...
Diameter of bigger ball = 8 cm radius of bigger ball = 4 cm \[Volume\text{ }=\text{ }4/3\text{ }\pi {{r}^{3}}~=\text{ }4/3\text{ }\pi \text{ }{{4}^{3}}~=\text{ }265\pi /3\text{ }c{{m}^{3}}\] Radius...
Let the radius of the spherical ball = r the volume = 4/3 πr3 And, the radius of smaller ball = r/2 Volume of smaller ball \[=\text{ }4/3\text{ }\pi {{\left( r/2 \right)}^{3}}~=\text{ }4/3\text{...
Volume of the sphere = 38808 cm3 Let the radius of the sphere \[\begin{array}{*{35}{l}} =\text{ }r \\ 4/3\text{ }\pi {{r}^{3}}~=\text{ }38808 \\ 4/3\text{ x }\left( 22/7 \right)\text{ x...
Surface area of the sphere = 2464 cm2 Let the radius of the sphere be r. surface area of the sphere \[\begin{array}{*{35}{l}} =\text{ }4\pi {{r}^{2}} \\ 4\pi {{r}^{2}}~=\text{ }2464 \\ 4\text{ x...
Let slant height of the first cone = l So, the slant height of the second cone = 2l Radius of the first cone = r1 And, the radius of the second cone = r2 Curved surface area of first cone = πr1l...
Let radius of each cone = r Given that, ratio between their slant heights = 5: 4 Let slant height of the first cone = 5x And slant height of second cone = 4x So, curved surface area of the first...
Let radius of cone y = r radius of cone x = 3r volume of cone y = V Then, volume of cone x = 2V Let h1 be the height of x and h2 be the height of y. \[\begin{array}{*{35}{l}} Volume\text{ }of\text{...
The ratio between radius and height = 5: 12 Volume of the right circular cone = 2512 cm3 Let its radius (r) = 5x, its height (h) = 12x and slant height = l \[\begin{array}{*{35}{l}}...
Circumference of the base (c) = 66 m Height of the conical tent (h) = 12 m Radius \[=\text{ }c/2\pi \text{ }=\text{ }66/\text{ }2\pi \text{ }=\text{ }\left( 33\text{ x }7 \right)/22\text{ }=\text{...
Curved surface area of the cone = 12320 cm2 Radius of the base = 56 cm Let the slant height be ‘l’ Curved surface area \[\begin{array}{*{35}{l}} =\text{ }\pi rl\text{ }=\text{ }12320\text{...
Slant height of the cone (l) = 17 cm Base radius (r) \[\begin{array}{*{35}{l}} =\text{ }8\text{ }cm \\ {{l}^{2}}~=\text{ }{{r}^{2}}~+\text{ }{{h}^{2}} \\ {{h}^{2}}~=\text{ }{{l}^{2}}~-\text{...
Height of the cylinder box = h = 35 cm Base radius of the cylinder box = r = 10 cm Width of metal sheet = 1m = 100 cm Area of metal sheet required = total surface area of the box Length x width =...
Let the original dimensions of the solid right cylinder be radius (r) and height (h) in cm. Then its volume = πr2h cm3and curved surface area = 2πrh Now, after the changes the new dimensions are:...
The radius of a solid right cylinder (r) = 100 cm let the height of a solid right circular cylinder (h) = 100 cm The volume (original) of a solid right circular cylinder \[\begin{array}{*{35}{l}}...
The ratio between height and radius of a cylinder = 3:1 Volume = 1029π cm3 …….(i) the radius of the base = r Then, it’s height will be = 3r Volume \[\begin{array}{*{35}{l}} =\text{ }\pi...
Length of the open pipe = 50 cm Its external diameter = 20 cm It’s external radius (R) = 10 cm Its internal diameter = 6 cm => It’s internal radius (r) = 3 cm Surface area of pipe open from both...
Internal radius of the cylindrical container = 10 cm = r Height of water = 7 cm = h So, the surface area of the wetted surface \[\begin{array}{*{35}{l}} =\text{ }2\pi rh\text{ }+\text{ }\pi...
Diameter of cylindrical container = 42 cm it’s radius (r) = 21 cm Dimensions of rectangular solid = 22cm x 14cm x 10.5cm The volume of solid = 22 x 14 x 10.5 cm3 ….. (i) Let the height of water = h...
Inner radius of the pipe = r = 5/2 = 2.5 cm External radius of the pipe = R = Inner radius of the pipe + Thickness of the pipe \[=\text{ }2.5\text{ }cm\text{ }+\text{ }0.5\text{ }cm\text{ }=\text{...
The diameter of the cylinder = 20 cm the radius (r) = 10 cm and the curved surface area = 100 cm2 Height = h cm (i) Curved surface area \[\begin{array}{*{35}{l}} =\text{ }2\pi rh \\ 2\pi rh\text{...
External diameter of hollow cylinder = 20 cm So, it’s radius = 10 cm = R Thickness = 0.25 cm the internal radius \[=\text{ }\left( 10\text{ }-\text{ }0.25 \right)\text{ }=\text{ }9.75\text{...
Radius of the well = 2.8/2 = 1.4 m Depth of the well = 28 m Hence, the volume of earth dug out \[\begin{array}{*{35}{l}} =~\pi {{r}^{2}}h \\ =\text{ }\left( 22/7 \right)\text{ x }1.4\text{ x...
Base circumference of cylinder (c) = 8 cm So, the radius \[=\text{ }c/2\pi \text{ }=\text{ }\left( 8\text{ x }7 \right)/\text{ }\left( 2\text{ x }22 \right)\text{ }=\text{ }14/11\text{ }cm\] Length...
The inner radius of the pipe = 2.1 cm Length of the pipe = 12 m = 1200 cm Volume of the pipe \[\begin{array}{*{35}{l}} =\text{ }\pi {{r}^{2}}h\text{ }=\text{ }22/7\text{ x }{{2.1}^{2}}~x\text{...
Since, a circular cylinder whose Height, h = 20 cm and base radius, r = 7 cm (i) Volume of cylinder \[\begin{array}{*{35}{l}} =\text{ }\pi {{r}^{2}}h\text{ }=\text{ }22/7\text{ }x\text{...