Volume And Surface Area - Study Mode

[#41] The radius of base and curved surface area of a right cylinder is 'r' units and 4πrh square units respectively. The height of the cylinder is :
Correct Answer

(C) 2h units

Explanation

Solution: Radius of the base = r units Curved surface area of a right cylinder = $$4pi { ext{r}}h$$ Curved surface area of cylinder = $$2pi { ext{RH}}$$ ∴ According to the question, $$2pi { ext{rH = }}4pi { ext{rh}}$$ ⇒ Height of cylinder = 2h units

[#42] A rectangular paper of 44 cm long and 6 cm wide is rolled to form a cylinder of height equal to width of the paper. The radius of the base of the cylinder so rolled is :
Correct Answer

(C) 7 cm

Explanation

Solution: Length of rectangle paper = Circumference of the base of cylinder If r is the radius of the cylinder : $$eqalign{
& Rightarrow 44 = 2pi r cr
& Rightarrow r = frac{{44 imes 7}}{{2 imes 22}} cr
& Rightarrow r = 7,cm cr} $$

[#43] A school room is be built to accommodate 70 children so as to allow 2.2 m 2 of floor and 11 m 3 of space for each child. If the room be 14 metres long, what must be its breadth and height ?
Correct Answer

(B) 11 m, 5 m

Explanation

Solution: Let the breadth and height of the room be b and h metres respectively. Then, Area of the floor $$ = left( {14b}
ight),{m^2}$$ $$eqalign{
& herefore 14b = 2.2 imes 70 cr
& Rightarrow b = frac{{2.2 imes 70}}{{14}} cr
& Rightarrow b = 11 cr} $$ Volume of the room : $$eqalign{
& = left( {14 imes 11 imes h}
ight){m^3} cr
& = left( {154h}
ight){m^3} cr} $$ $$eqalign{
& herefore 154h = 11 imes 70 cr
& Rightarrow h = frac{{11 imes 70}}{{154}} cr
& Rightarrow h = 5 cr} $$

[#44] A rectangular water tank is open at the top. Its capacity is 24 m 3 . Its length and breadth are 4 m and 3 m respectively. Ignoring the thickness of the material used for building the tank, the total cost of painting the inner and outer surface of the tank at the rate of Rs. 10 per m 2 is :
Correct Answer

(D) Rs. 800

Explanation

Solution: Depth of the tank : $$eqalign{
& = left( {frac{{24}}{{4 imes 3}}}
ight)m cr
& = 2,m cr} $$ Since the tank is open and thickness of material is to be ignored, we have Sum of inner and outer surface : $$eqalign{
& = 2left[ {left{ {2left( {l + b}
ight) imes h}
ight} + lb}
ight] cr
& = 2left[ {left{ {2left( {4 + 3}
ight) imes 2}
ight} + 4 imes 3}
ight]{m^2} cr
& = 80,{m^2} cr} $$ ∴ Cost of painting : $$eqalign{
& = { ext{Rs}}{ ext{.}}left( {80 imes 10}
ight) cr
& = { ext{Rs}}{ ext{. 800}} cr} $$

[#45] A swimming bath is 24 m long and 15 m broad. When a number of men dive into the bath, the height of the water rises by 1 cm. If the average amount of water displaced by one of the men be 0.1 cu.m, how many men are there in the bath ?
Correct Answer

(B) 36

Explanation

Solution: Volume of water displaced : $$eqalign{
& = left( {24 imes 15 imes frac{1}{{100}}}
ight){m^3} cr
& = frac{{18}}{5}{m^3} cr} $$ Volume of water displaced by 1 man = 0.1 m 3 ∴ Number of men : $$eqalign{
& = left( {frac{{frac{{18}}{5}}}{{0.1}}}
ight) cr
& = left( {frac{{18}}{5} imes 10}
ight) cr
& = 36 cr} $$