Question 11

A hemispherical tank full of water is emptied by a pipe at the rate of 3 (4/2) litres
per second. How much time will it take to empty half the tank, if it is 3m in
diameter? (Take π =22/7)

Solution

ANS: Radius of the hemispherical tank = (3/2)m
Volume of the tank =( 2/3)( 22/7)( 3/2)3m3=(99/14) m3
So,the volume of the water to be emptied =(1/2)x(99/14) m3=(99/28)x1000
litres =(99000/28) litres
Since, 25/7 litres of water is emptied in 1 second, 99000/28 litres of water
will be emptied in (99000/28)x(7/25) seconds, i.e., in 16.5 minutes.

Question 12

Given that 1 cu cm of marble weight 25g, the weight of a marble block of 28 cm in width and
5 cm thick, is 112 kg. Find the length of the block.

Solution

= 32 cm

Question 13

A rectangular block 6 cm X 12 cm X 15 cm is cut into exact number of equal cubes. What is
the least possible number of cubes?

Solution

Number of cubes =40

Question 14

Shown below is a cake that Subodh is baking for his brother’s birthday. The
cake is 21cm tall and has a radius of 15 cm. He wants to surprise his brother by
filling gems inside the cake. In order to do that, he removes a cylindrical
portion of cake out of the center as shown. The piece that is removed is 21 cm
tall.
If the cake weighs 0.5 g per cubic cm and the weight of the cake that is left
after removing the central portion is 6600 g, find the radius of the central
portion that is cut. Show your steps.
(Note: Take 𝜋 = 22/7)

Solution

Vol of cake without hole = π r² h = 22/7 x 15 x 15 x 21= 14850 cm³
Wt. of cake without hole = 14850 x 0.5 = 7425 g
Wt. of central hole = (Wt. of cake without hole) – (Wt. of cake after hole)
= 7425 -6600 = 825 g
Vol of cake with hole = 825/0.5 = 1650 cm³
π r2 h = 1650 cm³
22/7 x r²x 21 = 1650
On solving, radius of central portion = 5 cm

Question 15

A Semi-circular waffle sheet of radius 5 cm is folded into an ice-cream cone as
shown below.
(Note: The figures are not to scale)
Due to overlap while folding, the radius of the base of the cone is 80% of what
it would be without overlap.
Find the approximate volume of the cone. Show your work.
(Note: Take 𝜋 = 22/7 )

Solution

Vol of cone = 1/3 π r² h = (1/3) x (22/7) x 2 x 2 x 5 = 20 cm³

Question 16

The surface area of a cube is 96 cm². Find the length of its diagonal.

Solution

d = √48 ≈ 6.93 cm

Question 17

How many spherical lead shots of diameter 3 cm can be made out from a solid cube of lead
of dimensions 9𝑐𝑚 × 11𝑐𝑚 × 12𝑐𝑚?

Solution

84

Question 18

Marbles of diameter 1.4 cm are dropped into cylindrical beaker of diameter 7 cm containing
some water. Find the number of marbles that should be dropped into the beaker so that the
water level rises by 5.6 cm.

Solution

150

Question 19

A wall 24 m long, 0.4 m thick and 6 m high which is constructed with the bricks, each of
dimensions 25 𝑐𝑚 × 16 𝑐𝑚 × 10 𝑐𝑚. If the mortar occupies 1/10𝑡ℎ of the volume of the wall,
then find the number of bricks used in constructing the wall.

Solution

12960

Question 20

A hemispherical tank full of water is emptied by a pipe at the rate of 3(4/7)litres per second.
How much time will it take to empty the tank, if it is 3 m in diameter? (Take 𝜋 =22/7)

Solution

327.4cm³

SELF ASSESSMENT

Q1. A medicine capsule is in the shape of a cylinder of diameter 0.5cm with two hemispheres stuck to each of its ends. The length of the entire capsule is 1.4 cm. What is capacity of the capsule?

Q2. A medicine capsule is in the shape of cylinder with two hemispheres stuck to each of its ends (see the given figure). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area. [Use π = 22/7]

Q3. A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that 1/8 space of the cube remain unfilled. Thus find the number of marbles that the cube can be accommodated .

Q4. Two cubes, each of side 4 cm are joined end to end. Find the surface area of the resulting
cuboid.

Q5. The radii of the circular ends of a bucket of height 15 cm are 14 cm and r сm (r < 14 cm). If
the volume of bucket is 5390 cm³ , then find the value of r. [Use π = 22/7]

Q6. Two cubes each of volume 27 cm³ are joined end to end to form a solid. Find the surface area
of the resulting cuboid?