Volume And Surface Area - Study Mode

[#86] The ratio of the surface area of a sphere and the curved surface area of the cylinder circumscribing the sphere is :
Correct Answer

(A) 1 : 1

Explanation

Solution: Let the radius of the sphere be r Then, radius of the cylinder = r Height of the cylinder = 2r Surface area of sphere = $$4pi {{ ext{r}}^2}$$ Surface area of the cylinder = $$2pi { ext{r}}(2r) = 4pi {{ ext{r}}^2}$$ ∴ Required ratio : = $$4pi {{ ext{r}}^2}$$ : $$4pi {{ ext{r}}^2}$$ = 1 : 1

[#87] A hemispherical bowl of internal radius 12 cm contains liquid. This liquid is to be filled into cylindrical container of diameter 4 cm and height 3 cm. The number of containers that is necessary to empty the bowl is :
Correct Answer

(B) 96

Explanation

Solution: Volume of hemispherical bowl : $$ = left( {frac{2}{3} imes pi imes 12 imes 12 imes 12}
ight)c{m^3}$$ Volume of 1 cylindrical container : $$ = left( {pi imes 2 imes 2 imes 3}
ight)c{m^3}$$ ∴ Number of containers required : $$eqalign{
& = frac{2}{3} imes frac{{12 imes 12 imes 12}}{{2 imes 2 imes 3}} cr
& = 96 cr} $$

[#88] Length of each edge of a regular tetrahedron is 1 cm. It volume is :
Correct Answer

(D) $$frac{1}{{12}}sqrt 2 { ext{ }}c{m^3}$$

Explanation

Solution: Length of each edge of a regular tetrahedron = 1 cm Volume of regular tetrahedron : $$eqalign{
& = frac{{{a^3}}}{{6sqrt 2 }}{ ext{ c}}{{ ext{m}}^3} cr
& = frac{1}{{6sqrt 2 }} cr
& = frac{{sqrt 2 }}{{6sqrt 2 imes sqrt 2 }}{ ext{ c}}{{ ext{m}}^3} cr
& = frac{{sqrt 2 }}{{12}}{ ext{ Or }}frac{1}{{12}}sqrt 2 { ext{ c}}{{ ext{m}}^3} cr} $$

[#89] The base of a right prism is a trapezium whose lengths of two parallels sides are 10 cm and 6 cm and distance between them is 5 cm. If the heights of the prism is 8 cm, its volume is :
Correct Answer

(A) 320 cm 3

Explanation

Solution: Length of parallel sides of prism = 10 cm and 6 cm Height of prism = 8 cm ∴ Volume of prism : $$eqalign{
& = frac{1}{2}left( {10 + 6}
ight) imes 5 imes 8 cr
& = frac{1}{2} imes 16 imes 5 imes 8 cr
& = 320{ ext{ c}}{{ ext{m}}^3} cr} $$

[#90] A rectangular water reservoir contains 42000 litres of water. If the length of reservoir is 6 m and breadth of the reservoir is 3.5 m, then the depth of the reservoir will be :
Correct Answer

(A) 2 m

Explanation

Solution: Volume of the reservoir = 42000 litres = 42 m 3 Let the depth of the reservoir be h metres then, $$eqalign{
& 6 imes 3.5 imes h = 42 cr
& Or,,h = frac{{42}}{{6 imes 3.5}} = 2,m cr} $$