Conversion of Solid from One Shape to Another | Surface Areas and Volumes | Assessment | English | Grade 10

State whether the following statement is True or False. When a solid is converted from one shape to another, the volume of the new solid will be less than the volume of the original solid.

• TRUE

• FALSE

Answer explanation

We know that, During the conversion of a solid from one shape to another,the volume of the new solid will be equal to the volume of the original solid. Hence, the given statement is False.

Tags

CCSS.7.G.B.6

A solid cube of side 12 cm is cut into 8 cubes of equal volume. The side of the new cube is _______

• 12 cm

• 6 cm

• 3 cm

• 9 cm

Answer explanation

We know that, Volume of a cube = side³ Given: Side = 12 cm Volume of cube = 12³ = 1728 cm³ Number of small cubes = 8 Volume of small cube = 1728/8 = 216 cm³ Let side of small cube = a Volume of small cube = a³ = 216 cm³ a = ³√ 216 = 6 cm Hence the correct answer is option 2.

Tags

CCSS.5.MD.C.5A

CCSS.6.G.A.2

How many spherical lead shots each having a diameter of 3 cm can be made from a cuboidal lead solid of dimensions 9 cm x 11 cm x 12 cm ?

• 10

• 168

• 84

• 48

Answer explanation

We know that, Volume of a cuboid = lbh = 9 x 11 x12 = 1188 cm³ Given : Diameter of lead shot = 3 cm Radius of lead shot = 1.5 cm Volume of one lead shot = 4/3πr³ = 4/3 x 22/7 x 1.5 x 1.5 x 1.5 = 14.14 cm³ Number of lead shots = Volume of cuboid/Volume of one lead shot = 1188 / 14.14 = 84 shots Hence, the correct answer is Option 3

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

The surface area of a solid metallic sphere is 616 cm². It is remelted and cast into a cone of height 28 cm. Find the diameter of the base of the cone so formed.

• 7 cm

• 14 cm

• 49 cm

• 98 cm

Answer explanation

Surface Area of Sphere = 4πr² = 616 cm² so, r² = 616 / 4π = 49 cm² r = 7 cm Volume of sphere = (4/3) π r³ = (4/3) π 7³ Volume of cone = (1/3) πr² h Volume of cone = Volume of sphere (1/3) πr² h = (4/3) π 7³ r² h = 4 . 7³ r² 28 = 4 . 7³ r² = (4 . 7³) / 28 = 49 r = √49 = 7 cm So, diameter of cone = 2 x 7 = 14 cm Hence the correct answer is Option 2.

A farmer connects a pipe of internal diameter 25 cm from a canal into a cylindrical tank in his field, which is 12m in diameter and 2.5 m deep.If water flows through the pipe at 3.6 km/hr, in how much time will the tank be filled?

• 92 min

• 69 min

• 94 min

• 96 min

Answer explanation

Given : Radius of pipe = 12.5 cm = 0.125m Diameter of cylindrical tank= 12m Radius of Cylindrical tank = 6 m Height of Cylindrical tank = 2.5 m Volume of tank = πr²h = π6²2.5= 90π m³ Speed of water = 3.6 km/hr In 1 hour, length of water column = 3.6 km = 3600 m In 1 minute, length of water column = 3600 /60 m = 60 m Volume of water flowing through pipe in 1 minute = Volume of cylinder with radius 0.125 m cm and height 60 m = πr²h = π (0.125)²60 = π0.9375 m³ Time taken to fill the tank =Volume of tank/Volume of water flowing through pipe in 1 minute = 90π /π0.9375 = 96 minutes. Hence, the correct answer is Option 4.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3