SSC (English Medium) 10th Standard - Maharashtra State Board Question Bank Solutions for Geometry Mathematics 2

The radii of the ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its curved surface area.

The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its total surface area.

The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its volume \[\pi\] = 3.14) 

The circumferences of circular faces of a frustum are 132 cm and 88 cm and its height is 24 cm. To find the curved surface area of the frustum complete the following activity.( \[\pi = \frac{22}{7}\]) 

A washing tub in the shape of a frustum of a cone has a height of 21 cm. The radii of the circular top and bottom are 20 cm and 15 cm respectively. What is the capacity of the tub? ( \[\pi = \frac{22}{7}\]).

In right-angled triangle PQR, if ∠P = 60°, ∠R = 30° and PR = 12, then find the values of PQ and QR. 

In ΔDEF, if ∠E = 90°, then find the value of ∠D + ∠F. 

Choose the correct alternative: 
If the points, A, B, C are non-collinear points, then how many circles can be drawn which passes through points A, B, and C? 

In the above figure, the circles with P, Q, and R intersect at points B, C, D, and E as shown. Lines CB and ED intersect in point M. Lines are drawn from point M to touch the circles at points A and F. Prove that MA = MF. 

Out of given triplets, which is a Pythagoras triplet?

The diagonal of a square is `10sqrt(2)` cm then its perimeter is ______.

From the given figure, in ∆ABC, if ∠ABC = 90°, ∠CAB = 30°, AC = 14, then to find the value of AB and BC, complete the following activity.

Activity: In ∆ABC, if ∠ABC = 90°, ∠CAB = 30°

∴ ∠BCA = `square`

By theorem of 30° – 60° – 90° triangle,

∴ `square = 1/2` AC and `square = sqrt(3)/2` AC

∴ BC = `1/2 xx square` and AB = `sqrt(3)/2 xx 14`

∴ BC = 7 and AB = `7sqrt(3)`

From given figure, In ∆MNK, If ∠MNK = 90°, ∠M = 45°, MK = 6, then for finding value of MK and KN, complete the following activity.

Activity: In ∆MNK, If ∠MNK = 90°, ∠M = 45°   ...(Given)

∴ ∠K = `square`   ...(Remaining angle of ∆MNK)

By theorem of 45° – 45° – 90° triangle,

∴ `square = 1/sqrt(2)` MK and `square = 1/sqrt(2)` MK

∴ MN = `1/sqrt(2) xx square` and KN = `1/sqrt(2) xx 6`

∴ MN = `3sqrt(2)` and KN = `3sqrt(2)`

From the given figure, In ∆ABC, If AD ⊥ BC, ∠C = 45°, AC = `8sqrt(2)`, BD = 5, then for finding value of AD and BC, complete the following activity.

Activity: In ∆ADC, If ∠ADC = 90°, ∠C = 45°   ...(Given)

∴ ∠DAC = `square`   ...(Remaining angle of ∆ADC)

By theorem of 45° – 45° – 90° triangle,

∴ `square = 1/sqrt(2)` AC and `square = 1/sqrt(2)` AC

∴ AD =`1/sqrt(2) xx square` and DC = `1/sqrt(2) xx 8sqrt(2)`

∴ AD = 8 and DC = 8

∴ BC = BD + DC

= 5 + 8

= 13

As shown in figure, LK = `6sqrt(2)` then (1) MK = ? (2) ML = ? (3) MN = ?

How many circles can drawn passing through three non-collinear points?

How many circles can be drawn passing through a point?

The value of 2tan45° – 2sin30° is ______.

A milk container of height 16 cm is made of metal sheet in the form of frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of ₹ 22 per litre which the container can hold.